Development of a Reference Database for Beta-Delayed Neutron Emission
P. Dimitriou, I. Dillmann, B. Singh, V. Piksaikin, K.P. Rykaczewski, J.L. Tain, A. Algora, K. Banerjee, I.N. Borzov, D. Cano-Ott, S. Chiba, M. Fallot, D. Foligno, R. Grzywacz, X.Huang, T. Marketin, F. Minato, G. Mukherjee, B.C. Rasco, A. Sonzogni, M. Verpelli, A. Egorov, M. Estienne, L. Giot, D. Gremyachkin, M. Madurga, E.A. McCutchan, E. Mendoza, K.V. Mitrofanov, M. Narbonne, P. Romojaro, A. Sanchez-Caballero, N.D. Scielzo
DDevelopment of a Reference Database for Beta-Delayed Neutron Emission
P. Dimitriou, ∗ I. Dillmann,
2, 3
B. Singh, V. Piksaikin, K.P. Rykaczewski, J.L. Tain, A. Algora, K.Banerjee, I.N. Borzov,
9, 10
D. Cano-Ott, S. Chiba, M. Fallot, D. Foligno, R. Grzywacz,
15, 6
X.Huang, T. Marketin, F. Minato, G. Mukherjee, B.C. Rasco,
19, 6, 15, 20
A. Sonzogni, M. Verpelli, A. Egorov, M. Estienne, L. Giot, D. Gremyachkin, M. Madurga, E.A. McCutchan, E.Mendoza, K.V. Mitrofanov, M. Narbonne, P. Romojaro, A. Sanchez-Caballero, and N.D. Scielzo NAPC-Nuclear Data Section, International Atomic Energy Agency, A-1400 Vienna, Austria TRIUMF, Vancouver, British Columbia V6T 2A3, Canada Department of Physics and Astronomy, University of Victoria, Victoria, British Columbia V8P 5C2, Canada Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada State Scientific Center of Russian Federation, Institute of Physics and Power Engineering, 249033 Obninsk, Russian Federation Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA IFIC, CSIC-Universitat de Valencia, 46071 Valencia, Spain Variable Energy Cyclotron Centre, Kolkata 700064, India National Research Centre Kurchatov Institute, Department of Nuclear Astrophysics,1 Akademika Kurchatova pl., Moscow 123182, Russian Federation Joint Institute for Nuclear Research, Bogolubov Laboratory of Theoretical Physics,6 Joliot-Curie, 141980 Dubna, Moscow region, Russian Federation Centro de Investigaciones Energ´eticas, Medioambientales yTecnol´ogicas (CIEMAT), Avenida Complutense 40, Madrid 28040, Spain Tokyo Institute of Technology, 2-12-1-N1-9, Ookayama, Meguru-ku, Japan Subatech, CNRS/in2p3, Univ. of Nantes, IMTA, 44307 Nantes, France CEA, DEN, DER/SPRC/LEPh Cadarache, F-13108 Saint Paul-Lez-Durance, France Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA China Nuclear Data Center, China Institute of Atomic Energy, Beijing 102413, China Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia Nuclear Data Center, Nuclear Science and Engineering Center,Japan Atomic Energy Agency, Tokai-mura Ibaraki-ken, Japan JINPA, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA National Nuclear Data Center, Brookhaven National Laboratory, Brookhaven, Upton NY, USA Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California 94550, USA (Dated: February 3, 2021)Beta-delayed neutron emission is important for nuclear structure and astrophysics as well as forreactor applications. Significant advances in nuclear experimental techniques in the past two decadeshave led to a wealth of new measurements that remain to be incorporated in the databases.We report on a coordinated effort to compile and evaluate all the available β -delayed neutron emis-sion data. The different measurement techniques have been assessed and the data have been com-pared with semi-microscopic and microscopic-macroscopic models. The new microscopic databasehas been tested against aggregate total delayed neutron yields, time-dependent group parametersin 6-and 8-group re-presentation, and aggregate delayed neutron spectra. New recommendations ofmacroscopic delayed-neutron data for fissile materials of interest to applications are also presented.The new Reference Database for Beta-Delayed Neutron Emission Data is available online at: . CONTENTS
I. INTRODUCTION 2II. MICROSCOPIC DATA: Methods andmeasurements 4A. Delayed neutron emission probabilities 41. Beta-neutron coincidences (“ β –n”) 62. Neutron and β counting (“n, β ”) 73. Relative neutron counting (“ P n A Z”) 8 ∗ Corresponding author: [email protected]
4. Neutron counting per fission (“fiss,n”) 85. Neutron and γ counting (“n, γ ”) 86. Double γ counting (“ γ , γ ”) 87. Ion and neutron counting (“ion,n”) 98. Double ion counting (“ion,ion”) 9B. Delayed neutron spectra 91. He spectrometers 92. Gaseous proton recoil spectrometers 103. Neutron energy spectroscopy withtime-of-flight spectrometers 10C. New methods (for P n values and energyspectra) 111. Total absorption γ -ray spectroscopy 11 a r X i v : . [ nu c l - e x ] F e b evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
2. Ion-recoil methods 123. Optical Time Projection Chamber 124. Measurement in a storage ring 125. Ion counting using a MR-TOF 13D. Outlook for future measurements 13III. COMPILATION AND EVALUATION 14A. Compilation and evaluation methodology 14B. New evaluated ( T / , P n ) data 141. Z = 2 – 28 region 142. Z = 29 – 57 region 173. Z = 58 – 87 region 17C. P n Standards 17D. Systematics for P n values 171. Kratz-Herrmann formula 182. McCutchan systematics 183. Improved systematics along Z chains 184. Systematics based on the EffectiveDensity Model 18E. Delayed neutron spectra for individualprecursors 191. Digitization of delayed neutron (DN)energy spectra 192. Assessment of spectra as a reference forcalibration purposes 20IV. THEORY OF MICROSCOPIC DATA 20A. Self-consistent QRPA-based models 221. DF+CQRPA 222. Relativistic Density Functional+QRPA 22B. Comparison with new evaluated ( T / , P n )data for important β -delayed neutronemitters 231. Light fission products 232. Heavy fission products 24C. Comparison for isotopes relevant to nuclearastrophysics 241. β -decay properties in the Ni region 272. β -decay properties in the Sn region 28D. Global comparisons of theoretical results 30E. Delayed neutron spectra calculations 35V. MACROSCOPIC DATA: Methods andMeasurements 38A. Methods 381. Total delayed neutron yields andtime-dependent parameters 382. Delayed neutron integral spectra 41B. New measurements and compilation 411. Energy dependence of the relativeabundances and half-lives of delayedneutrons 422. Energy dependence of total delayedneutron yield 423. Integral energy spectra of delayedneutrons from fission of
U by thermalneutrons 444. ALDEN: new measurements of delayed neutron data 45C. Estimation of energy dependence of totaldelayed neutron yields 45VI. SUMMATION CALCULATIONS 50A. A numerical ( T / , P n ) data file for practicalapplications 50B. Total delayed neutron yields 511. Basic summation calculations 512. Time-dependent calculations 54C. Time-dependent delayed-neutron integralspectra 57D. Time-dependent delayed-neutronparameters 60VII. INTEGRAL CALCULATIONS 67A. Comparison with integral experiments 67B. Impact on reactor calculations 69VIII. SYSTEMATICS OF MACROSCOPIC DATA:Time-dependent parameters 71A. New approach for estimation of temporaryparameters for unmeasured nuclides 71B. The ( A c /Z ) ·
92 systematics of the averagehalf-life 72C. Systematics ( A c − · Z ) of relativeabundances in the 8-group model 72IX. RECOMMENDED DATA IN 6- and 8-GROUPMODELS 72X. REFERENCE DATABASE 79A. Microscopic data 80B. Macroscopic data 80XI. SUMMARY AND CONCLUSIONS 80A. Microscopic experiments 84B. Compilation and evaluation of microscopicdata 84C. Microscopic theory 85D. Summation and time-dependentcalculations 86E. Integral experiments and reactorcalculations 86F. Macroscopic measurements andsystematics 86G. New recommendations of group constants 87Acknowledgments 87References 88 I. INTRODUCTION
Neutron-rich nuclei can emit neutrons after β -decay when their decay Q -value is larger than the(one/two/three. . . ) neutron separation energy: Q β >S xn . This decay mode is called “ β -delayed ( β n) neu-2evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al. tron emission” and was discovered in 1939 by Roberts etal. [1, 2], shortly after the discovery of fission by Meit-ner, Hahn, and Strassmann in 1938 [3]. Immediately af-ter this, Bohr and Wheeler [4] improved their liquid dropmodel to describe these new decay mechanisms.The β -delayed two- and three-neutron emission ( β β Li[5, 6], and in 1988 the (so far) only β
4n emitter, B,has been investigated and a tentative branching ratio of P n = 0 . β -decay half-life of the precursor A Z ,ranging from a few milliseconds for the most neutron-rich isotopes up to 80(18) s for Tl, the longest-lived β -delayed neutron ( β n) precursor observed to date.These delayed neutrons have to be distinguished from theprompt neutrons evaporated immediately (in the order of10 − s) after a fission event from a neutron-rich nucleusand usually form only a small fraction of the total neu-trons emitted from fission ( ≈ U, they found that by groupingthe β n emitters in six groups – according to their half-lives – they could reproduce the experimental data.In 1990, Subgroup 6 was established by the NEA-OECD “Working Party on International Nuclear DataEvaluation Co-operation” (WPEC-SG6) [14] to assess thedifferences between the calculated and measured values ofthe reactivity scale obtained from reactor kinetics. Theobserved discrepancies were largely attributable to theuncertainties in the delayed neutron data used in thesecalculations. Their effort to address this included interna-tional benchmark measurements of the effective delayedneutron fraction, made on fast critical assemblies, whichaimed to provide high-quality experimental informationfor U, U, and
Pu.One of the outcomes of this working group was the re-finement of the Keepin parameters by the laboratories inLos Alamos and Obninsk from a 6-group fit to an 8-groupfit. This was achieved by separating the three longest-lived delayed neutron precursors ( Br,
I, and Br)into single groups.Independent of the effort to determine integral delayedneutron yields for applications, there have also been sev-eral attempts to measure, compile and evaluate β -delayedneutron data of individual precursors. Groups in Swe-den [15, 16], USA [17, 18], and Germany [19] becameactive in measurements of β -delayed neutron probabil- ities and spectra in the late 1970s. A large number ofdata was published in the following decades and subse-quently compiled and evaluated by Rudstam and collab-orators [15, 16, 20, 21] and Pfeiffer et al. [22].Values from these compilations and evaluations havesometimes been incorporated in ENSDF [23], togetherwith independent recommendations by the respec-tive evaluator. Consequently, these values have alsobeen transferred to evaluated data libraries such asENDF/B [24, 25], JENDL [26, 27] and JEFF [28, 29]decay-data libraries, as well as in nuclear astrophysicsapplications. Other independent evaluations have alsobeen performed to address specific needs in applica-tions, such as the highly-specific evaluations of decaydata for short- to very short-lived radioisotopes, includ-ing β -delayed neutron emitters, which were performedfrom 1996 to 1998 by Nichols [30] for the UK-based datafile. These evaluations were subsequently adopted in theJEFF decay-data libraries [29].The first comprehensive compilation and evaluation of β -delayed neutron emission spectra was published byBrady [31] in an effort to combine measured spectra withstatistical model calculations to complete the experimen-tal data that was sometimes scattered or limited in en-ergy range. The resulting spectra were adopted in theENDF/B libraries and were further supplemented withmodel calculations by Kawano et al. [32].Until 2011 only sporadic efforts have been made tocollect data of ‘microscopic’ quantities related to the β -delayed neutron emission, namely half-lives and neutron-branching ratios of very neutron-rich nuclei to reveal nu-clear structure properties for nuclei far from stability.This data has also been used directly as nuclear physicsinput for astrophysical reaction network calculations forthe ”rapid neutron capture” ( r ) process in explosive as-trophysical scenarios like core collapse supernovae andbinary neutron star mergers, or indirectly to benchmarkand improve theoretical predictions which are needed forextrapolating models towards the yet inaccessible regionsof the nuclide chart (“Terra Incognita”).Recent experimental efforts relied largely on the exist-ing generation of radioactive beam (RIB) facilities butwith the next generation of these facilities becoming op-erational within this decade, a plethora of new nuclideswill become accessible. The vast majority of these newnuclides on the neutron-rich side will be β n-emitters.According to the Atomic Mass Evaluation in 2016(AME2016) [33], 651 out of the 3435 known nuclei are β n emitters, meaning that their Q β n is (within massuncertainties) positive. Theoretical models estimate thatabout 4000 additional nuclei should exist between theproton- and neutron dripline, most of them are on theneutron-rich side and will be β n emitters.In 2011, 72 years after the discovery of β -delayed neu-trons , only 216 β n emitters had measured neutron-branching ratios: 81 nuclei in the lighter mass region( Z < Z = 29 −
57, and a single (unconfirmed) measurement3evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al. of the P n value of Tl [34] in the whole mass regionabove
Z > Heand
Ac have been identified as potential β -delayed one-neutron emitters ( Q β n > β -delayedone-neutron branching ratios ( P n ): 114 in the light massregion Z <
28 [35], 183 in the fission fragment region( Z = 29 − Z >
57 [36].A total of 28 of these measurements provided only anupper limit for the P n value, and another six providedonly lower limits.As far as delayed multi-neutron emission is concerned,300 potential β β β P n values have been measured(23 for Z <
28 and eight for
Z >
28) and four P n values( Li, B, B, and N). One single tentative measure-ment for the P n value of B has been reported.One of the largest and most focused recent efforts tofill this large gap between identified and measured β -delayed neutron branching ratios is the ”Beta-delayedneutrons at RIKEN” (BRIKEN) project [37]. Since 2016this international collaboration has been measuring half-lives and neutron-branching ratios of almost all accessible β n emitters. The collaboration will conclude its experi-mental campaigns in 2021 and is expected to add in thenear future >
250 new β -delayed neutron emitters tothe existing list. The data from the experimental runsin 2016–19 is presently being analyzed, and a small frac-tion has already been published and included in the latest Z >
28 evaluation [36]. An overview of the BRIKEN andfuture campaigns can be found in Sect. II D.This rapidly developing landscape of measured β n emitters and respective application-driven needs forreliable β n data necessitates both, a thorough update ofthe existing β n-data compilations and a review of therecommended group parameters. In response to these ur-gent data needs, the International Atomic Energy Agency(IAEA) coordinated an international effort to produce a‘Reference Database of Beta-Delayed Neutron EmissionData’ [39–42].The results of this coordinated effort are reported inthis paper. The methods for measurement of microscopic β -delayed neutron data are described in Sect. II, fol-lowed by the compilation and evaluation efforts (includ-ing new recommendations of standards for P n measure-ments) and systematic descriptions in Sect. III. Compar-isons of the β -delayed neutron data (half-lives, β -delayedneutron -branching ratios and spectra) with global theo-retical approaches are presented in Sect. IV.Macroscopic (integral) delayed neutron yields andspectra have been used to verify and validate the mi-croscopic data. Measurement methods, new data, andcompilation efforts are presented in Sect. V. Summationand time-dependent calculations of total delayed neutronyields and spectra based on the evaluated microscopic β - delayed neutron data are described and compared withrecommended values in Sect. VI. The impact of the new β -delayed neutron data on integral reactor calculationsis discussed in Sect. VII. Finally, the systematics of themeasured macroscopic data are discussed in Sect. VIIIand new recommendations for 6- and 8-group kineticparameters for major and minor actinides are given inSect. IX.The structure of the reference database is detailed inSect. X and a summary of the main conclusions of thiswork is provided in Sect. XI.All the microscopic and macroscopic data presentedherein, are available online at [43]. II. MICROSCOPIC DATA: METHODS ANDMEASUREMENTSA. Delayed neutron emission probabilities
The neutron-branching ratio of a nucleus into the β P n = N n N decays . (1)where N n stands for the number of decays ( N decays )that emit one neutron. Similar expressions hold for anyother β -delayed multi-neutron decay channel. This quan-tity can be measured in various ways with different tech-niques, either directly by counting the number of emit-ted neutrons, or indirectly by counting γ -rays or otherdecay products. Special care has to be taken that thenumber of counted events are free of any contaminations,i.e. that the contributions from background activities aresubtracted and the random noise is properly correctedfor.Eight methods for the determination of P n values wereextracted from the previous Rudstam evaluation [21] andwere reviewed in the IAEA CRP summary reports [39–41] for their strengths and weaknesses and, in particular,potential sources of systematic errors and uncertainties.These methods were complemented by newer methods.Note that only a few of these methods are also suited forthe measurement of multi-neutron emission probabilities.Throughout this article the following notation will beused: precursor ( A Z) or mother nucleus stands for the β -decaying nucleus; β -decay daughter or intermediate nu-cleus is the product from the β decay of the precursor( A Z+1), and β -delayed neutron daughter stands for thefinal nucleus with A − Z+1 for the case of one-neutronemission, A − Z+1 for the case of two-neutron emission,etc.The majority of P xn values in the literature have beendetermined using methods that involve neutron count-ing using moderated neutron detectors. These type ofcounters combine a medium acting as a neutron energy4evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 1. Chart of nuclides with color-coded Q βn window (in keV, retrieved from NuDat 2.7 [38]). moderator with a detector sensitive to thermal neutronsto maximize detection efficiency. Typical moderators aremade of dense hydrogenated material, like high-densitypolyethylene that has replaced the paraffin wax of earlierdesigns. The first counters used BF -filled proportionaltubes as a thermal neutron detector, but nowadays themore expensive He is preferred because of its advantages[44] (see also Sect. II B). This detector can be consideredas an evolution of the neutron long counter [45], wherevery high detection efficiencies are achieved by arrangingseveral tubes in a 4 π geometry around the source. Apartfrom the large detection efficiency, another distinct ad-vantage of this type of detector is the virtual absence ofa low-energy threshold.Recent examples of this kind of setup applied to themeasurement of P xn are NERO (now HABANERO)at the National Superconduction Laboratory (NSCL)at Michigan State University (USA) [46], LOENIE atLohengrin-Institute Laue Langevin (France) [47], 3Henat HRIBF-Oak Ridge National Laboratory (USA) [48],BELEN at the GSI Helmholtz Center for Heavy Ion Re-search in Darmstadt (Germany) and at the heavy ion ac-celerator laboratory of the University of Jyv¨askyl¨a (Fin-land) [49], and TETRA at ALTO - Institute de PhysiqueNucleaire in Orsay (IPNO, France) [50]. The latest setupis BRIKEN at RIKEN Nishina Center in Wako (Japan)which is a temporary merger of the 3Hen and BELEN counters with some additional He tubes from RIKEN[37, 51].The detection efficiency of these type of detectors ex-hibits a dependency on neutron energy which can be asource of systematic uncertainty in the determination of P xn values (see discussion in II A 1). The effect is re-lated to the moderation process and depends on the ge-ometry of the counter (number and spatial distributionof neutron detectors). Thus the detector design can beoptimized to minimize the dependency of the efficiencyon neutron energy. An example of this is the LOENIEcounter [47]: With only 18 He tubes a very small (17%)but flat efficiency up to 2 MeV is achieved.Nowadays the general trend is to minimize the energydependency of the efficiency curve while still maximiz-ing the overall detection efficiency. This can be achievedby increasing the number of tubes considerably, as hasbeen done for example in the case of the BRIKEN setupwhich could use up to 166 He tubes. The optimization ofthe geometry incorporating many tubes is a complicatedproblem that can be solved by combining Monte Carlosimulations with a parametric approach [37]. In this waya configuration with an efficiency in excess of 75% below1 MeV was obtained that drops (only) to an efficiency of54% at 5 MeV.The efficiency calibration of these instruments requiresthe use of mono-energetic isotropic neutron sources span-5evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al. ning the range of neutron energies of interest to well above5 MeV for exotic nuclei [52]. Photo-neutron ( γ, n ) and α -induced reaction sources (like Am/ Be or x Cm/ C),as well as fission sources have been employed [53] butthese are difficult to prepare or have a very broad energyspectrum. Beam-induced ( p, n ) and ( α, n ) reactions havealso been used [46] although it seems difficult to reachthe required accuracy.In experiments at radioactive beam facilities β -delayedneutron emitters with well know P n values and neutronspectra are used for the efficiency calibration of the setup.For sources with a broad neutron energy distribution themeasured neutron detection efficiency is averaged overthe respective neutron energy range. However it shouldbe kept in mind that this is an approximation as differentneutron spectra – detected with different average efficien-cies – can have the same average energy. Thus, for thesesources the measurements should be combined with de-tailed Monte Carlo simulations, although the accuracy ofthe latter in complex geometries is still under discussion.The moderation process introduces a delay betweenneutron emission and detection that reaches few hun-dreds of µ s. This poses a problem for conventional trig-gered event-based data acquisition systems. The use ofan event gate of this length can lead to a sizable loss ofdata due to the acquisition dead time. This problem isovercome by modern event-less self-triggered data acqui-sition systems, as in the case of the most recent neutrondetection setups 3Hen, BELEN, TETRA, and BRIKEN.In the following, the eight different methods for obtain-ing P n values as well as their advantages and disadvan-tages are discussed.
1. Beta-neutron coincidences (“ β –n”) In this method β ’s and neutrons are counted in coinci-dence and compared with the number of β counts. Thusthe efficiency of the β detector is greatly reduced, whilethe neutron efficiency in absolute terms is needed. Thismethod was labelled “n/ β ” in Ref. [21] and has been re-named here to “ β –n” to account for the proper sequenceof emissions of the particles.For measuring the one-neutron emission probability( P n ), the respective equation is P n = 1 (cid:15) n N β n N β , (2)where (cid:15) n is the one-neutron detection efficiency, N β n is the number of time-correlated β -1n events, and N β isthe amount of detected β ’s. The main assumption in Eq.2 is that the detector efficiency for β decays is constant forall energies and thus cancels out. However, β detectorshave a lower threshold of typically 50–150 keV, and therespective efficiency curve shows a steep drop below ≈ He-neutron detector has an (almost) constant neutron detection efficiency for ener-gies up to 1 MeV, and then the curve drops slowly. Theseeffects might introduce systematic errors if the calibratingisotopes have very different β - or neutron-energy spectra[49]. Examples of efficiency curves for a typical β - andmoderated neutron detector used in experiments at theIGISOL facility in Jyv¨askyl¨a are shown in Fig. 2 [54]. Itcan be seen that the highest neutron energies are con-nected to low-energy β ’s with the lowest detection effi-ciency due to the detector thresholds, and vice versa.An additional source of uncertainty is that the energydependence (slope) of the neutron efficiency curve is oftenignored. However, if the neutron energy distribution ofthe calibrant isotope is very different to the one of theisotope to be measured, this will induce systematic effectswhich need to be corrected for. For moderated neutrondetectors the “average detection efficiency” depends onthe neutron energy spectra of each isotope. Fig. 3 showsthe neutron spectra of the β n emitters Br (green line), Rb (blue line), and
I (red line) as an example. Forcomparison, two simulated neutron detection efficiencycurves for two state-of-the-art neutron detectors, BELEN[54] and BRIKEN [37], are plotted as dashed lines.The correct description for the neutron-branching ratioshould therefore include detection efficiencies (cid:104) (cid:15) (cid:105) whichare averaged over the respective energy ranges: P n = (cid:15) β (cid:104) (cid:15) (cid:48) β · (cid:15) n (cid:105) N β n N β (3)In this equation (cid:15) β is the mean β efficiency. (cid:104) (cid:15) (cid:48) β · (cid:15) n (cid:105) isthe product of the averaged β efficiency above the neutronseparation energy weighted by the respective β intensityspectrum and the averaged neutron efficiency weightedby the neutron spectrum [49, 54]. If (cid:15) β = (cid:104) (cid:15) (cid:48) β (cid:105) , then thesimplified Eq. 2 is recovered.Even with this simplification, the method requires theknowledge of the neutron spectra of the respective isotopeto be measured (see Sect. II B). Since these spectra arenot available for all isotopes, one can use as a guidancethe spectra of calibration isotopes like the ones shown inFig. 3 and listed in Sections III C and III E, selected tocover the expected neutron energy range of the isotopesof interest.When analyzing decay curves the signals from all con-tributing decays need to be considered. This requires aproper knowledge of the different half-lives of all involvednuclei and possible isomeric states. In turn, if a half-lifein a decay chain is not know, this method can also be usedto extract the unknown half-lives of β n emitters from β -and β n-decay curves.Extensions of the “ β –n” method to include multi-neutron emission increase the complexity as the neutron-emission multiplicity (x) increases. Since the neutron-detection efficiency is < β xn decay channel willcontribute to the counts N βyn with y ≤ x [6] whichmust be taken into account. It is also important to in-clude corrections for accidental coincidences with back-ground neutrons, in particular when the background rate6evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 2. Examples of efficiency curves for a β - and a neutron detector [54] in comparison with an example neutron spectra. Notethat the highest neutron energies are connected to β ’s with the lowest detection efficiency due to the detector thresholds.FIG. 3. Examples of neutron spectra for Br (green), Rb(blue), and
I (red) in comparison with two (simulated) ef-ficiency curves for state-of-the art neutron detectors (dashedand dotted line) used in experiments at the IGISOL facilityin Jyv¨askyl¨a [54] and at RIKEN [37]. is large and the P xn value is small. The importance of aproper background correction has been discussed recentlyin Refs. [51, 54, 55]. As in the P n case (Eq. 3), the cor-rect expressions must include variable, isotope- and decaychannel-dependent β - and neutron-detection efficiencies.In summary, the “ β –n” method is a generic and widelyemployed method that is well-suited for the measurementof single- and multi-neutron-branching ratios . It is themethod of choice if the rate of neutrons from the respec-tive decay is small compared to the rate of background neutrons, since the coincidence relations will increase thesensitivity to the neutrons of interest. It is a reliablemethod if all pitfalls as described above are carefully con-sidered and accounted for. The main sources of system-atic uncertainty are the β and neutron detection efficien-cies that have to be simulated carefully.
2. Neutron and β counting (“n, β ”) In this method the β ’s and neutrons are counted si-multaneously but separately (not in coincidence). Thismethod was labelled “n– β ” in Ref. [21]. The P n valuecan be extracted from the ratio of counted events cor-rected by the ratio of detection efficiencies: P n = (cid:15) β (cid:15) n N n N β . (4)The “n, β ” method requires that either both efficien-cies are determined separately or that their ratio is ob-tained from calibration nuclei. All systematic errors on β and neutron detection efficiencies related to the differ-ent intensity distributions and the shape of the efficiencycurves discussed in the previous method apply also hereand have to be included properly. The β detection needsto be checked for potential sources of background, e.g.conversion electrons or changing noise in the detectors.This method is also quite generic and applicable to themeasurement of multiple neutron emission. The mainpractical limitation is the neutron signal-to-backgroundratio that can be overcome by the use of β -n coincidences(the “ β –n” method).7evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
3. Relative neutron counting (“ P n A Z”)
This is a neutron-only counting method and requiresthat in the decay chain either a descendant or the parent A Z is a β n-emitter with well known P n value which be-comes the normalization. In addition, all half-lives haveto be known including that of the measured precursorwhich could be determined independently from β activ-ity curves. It is based on the analysis of the measuredneutron activity curve to disentangle the different contri-butions. The method has been applied only in a few casesafter chemical or mass separation, thus activity curvesmust be corrected for contaminants. In its simplest formit assumes that the neutron energy spectrum (and thusthe neutron detection efficiency) for parent and descen-dants are identical but eventually corrections as discussedbefore should be applied.
4. Neutron counting per fission (“fiss,n”)
This method was labelled “fiss” in Ref. [21]. Histori-cally this is the oldest method used to measure neutronemission probabilities of individual precursors [56]. It isbased on the determination of the number of β -delayedneutrons per fission of a given precursor Y nA,Z with a suit-able neutron detector. This number is compared then tothe fission yield Y A,Z of that precursor to obtain the P n value: P n = Y nA,Z Y A,Z (5)Typically fission of
U at thermal neutron energieshas been used in these measurements. The main sourceof systematic error is the accuracy of the fission yieldsavailable at the time of the measurement. For example, inthe evaluation of Rudstam [21] the results of earlier stud-ies were updated using the fission yields Y A from Wahl[57] and the respective charge fraction P Z . However, newmass- and charge-dependent fission yields Y A,Z are nowavailable, e.g. from evaluated libraries like ENDF/B-VIII.0 and JEFF-3.1.1. Thus, a renormalization of theolder data to the new fission yields standards is advis-able.This method was applied mostly to chemically sepa-rated samples [21], a procedure that requires a certainprocessing time (in the order of 1 s) and is not suitedfor very short-lived β -delayed neutron emitters. It is af-fected by systematic uncertainties of the chemical separa-tion efficiency as well as the neutron efficiency. For olderexperimental data, the lack of separation of the differentisotopes and the presence of contaminants could have af-fected the determination of the P n value. Experienceshows that the reliability of this method can be poor andthat should be taken into account when comparing withother methods.
5. Neutron and γ counting (“n, γ ”) This method was called “ γ A Z” in [21] and is renamedto “n, γ ” method to account for the separate counting ofneutrons from the precursor and γ ’s from the daughter A Z decay ( A Z+1 in the nomenclature in this paper). Itshould not be confused with the “n– γ ” method in [21]which actually designates a “ γ , γ ” method (see below).Because of the usually much longer half-live of the daugh-ter it is convenient to measure first the neutron activityof the sample, and then the γ -activity in a separate ded-icated setup [58].The method requires that the absolute γ -intensity I absγ of one or more transitions in the decay of the daughteris known. Corrections for growth and decay of activities,which require a knowledge of half-lives, must be appliedbefore calculating the P n : P n − P n = (cid:15) γ · I absγ (cid:15) n N n N γ (6)The γ -ray detection efficiency (cid:15) γ is usually well known,thus the main issue is the availability and accuracy ofabsolute γ intensities per decay. If the daughter decayactivity is also co-produced and present in the sample,this needs to be accounted for. The method can be usedalso with γ -rays from subsequent descendants in the β -decay chain.
6. Double γ counting (“ γ , γ ”) This method involves counting of γ -rays emitted by de-scendants in both, the β -decay and the β xn-decay chains.The γ activities can be labeled by their masses, which inthe case of β
1n emitters are A and A-1, respectively. Themethod requires knowledge of the absolute γ -intensitiesper decay for both transitions used [59]. After correct-ing the γ counts by the growth and decay of activities,the possible branching-out/branching-in from/to the re-spective decay chains and the presence of contaminantactivities in the sample, the P n can be deduced from: P n − P n = (cid:15) Aγ · I abs,Aγ (cid:15) A − γ · I abs,A − γ N A − γ N Aγ (7)The main advantage of this technique lies in the rel-ative simplicity of detecting γ rays as compared to de-tecting neutrons, but the problem is shifted to the de-termination or knowledge of the absolute γ intensitiesper decay. The main drawback can be the low signal-to-background ratio requiring that the limited peak effi-ciency of γ -ray detectors is compensated by high count-ing statistics. Tagging with β particles can be used toimprove the sensitivity but at the cost of introducing apossible dependence on the β detection efficiency.8evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al. If β -decaying isomers are present with half-lives similarto the ground state, γ rays can provide a uniquely selec-tive tool to discriminate them, and measure correctly the P xn values of isomeric and ground states.Fragmentation facilities offer new opportunities for thistechnique, as descendants of the nucleus of interest A Z inthe β and β xn decay chains can be independently pro-duced and transmitted with the beam. In this case, ab-solute γ intensities for suitable transitions can be deter-mined in the same experiment using the number of im-planted ions for normalization [60]. However, the possibleexistence of isomers should be investigated, and the ac-tivity should be corrected according to the correlationtime. Since ions with different Z are implanted at dif-ferent depths in the respective implantation detector, β efficiency corrections might also be needed.The “ γ , γ ” method is suitable for the measurement ofmulti-neutron emission branches.
7. Ion and neutron counting (“ion,n”)
This corresponds to the “ion” method as defined in [21].It is based on the direct measurement of the number ofparent nuclei rather than the β ’s emitted. It has beenapplied at mass separators by counting the number of se-lected ions. For example, ions can be counted by implan-tation on an electron multiplier that is surrounded by theneutron detector [61]. In other arrangements two mea-surements are needed, one for counting the ions, wherethe beam is deflected to the electron multiplier, and onefor counting neutrons where the beam is implanted ina collector in the middle of the neutron detector [62].In this case, additional systematic uncertainties must beconsidered. The neutron emission probability is deter-mined as P n = (cid:15) ion (cid:15) n N n N ion . (8)Here N ion is the number of ions after correction forcontaminants and background and (cid:15) ion is the ion detec-tion efficiency. The determination of the ion detectionefficiency of the electron multiplier can be an issue asshown in [61].More recently (see [63] as an example), non-destructiveion counting with microchannel plates before implanta-tion has been applied to post-accelerated mass-separatedion beams. In this example however, γ counting of de-scendant decays was used instead of neutron counting toobtain the P n value (“ γ ,ion” method).
8. Double ion counting (“ion,ion”)
The “ion,ion” method is possibly the only new methodfor the measurement of β -delayed neutron emission prob-abilities that was developed in recent years, thanks to advances in instrumentation. It is based on counting di-rectly the number of parent nuclei and the number ofdaughter nuclei produced after neutron emission, circum-venting the direct neutron detection.The method includes several different techniques likedetecting recoils in a Beta-decay Paul trap (BPT) [64],observing recoil tracks with an optical time-projectionchamber (OTPC) [65], or separating and counting ionswith a heavy-ion storage ring [66] or a Multi-ReflectionTime-Of-Flight (MR-TOF) spectrometer [67]. With thefirst two methods it is also possible to extract neutronenergy spectra for the one-neutron emitters via the en-ergy of the recoil, but not in the case of multi-neutronemitters. More details can be found in Sect. II C. B. Delayed neutron spectra
Most of the available data on the spectra of β -delayedneutrons have been obtained using three different tech-niques: He spectrometers, gaseous proton recoil spec-trometers, and time-of-flight spectrometers. In the fol-lowing the principles, instruments, and analysis methodsof the three techniques are described. He spectrometers
This method is based on the detection of fast neutronsthrough the reaction n + He → p + H, which has apositive Q-value of 764 keV. In a He filled proportionaldetector the reaction leads to the appearance of a peakin the spectrum for mono-energetic neutrons. The neu-tron energy E n can be determined from the displacementof the observed peak with respect to the thermal neu-tron peak. For a continuum neutron energy distribution,the measured spectrum must be deconvoluted using theenergy-dependent neutron detector response.Following the introduction of high-pressure griddedionization chambers [68] with good energy resolution(10 −
20 keV) and efficiency, this method has been used tomeasure β -delayed neutron spectra of several fission sys-tems and individual precursors [31]. One disadvantageof this type of detector is the fast drop in efficiency withneutron energy: whereas at thermal energies the reactioncross section is as large as 5316 b it drops to 0.8 b at1 MeV. This imposes a practical limit in the maximummeasurable energy of about 3 MeV. In addition, the largepeak due to the thermal-epithermal neutron backgroundlimits the minimum measurable energy to about 100 keVor more.The accurate determination of the detector responseis an essential step in this method. This is typicallyachieved using mono-energetic neutrons from reactionslike Li(p , n) Be. The shape of the measured responsedeparts from that of a simple peak due to several ef-fects. Apart from electronic and microphonic noise, theresponse includes the effect of γ -ray interactions (includ-9evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al. ing pulse pile-up), a peak due to thermal neutron back-ground, the effect of neutron-induced recoils in the gas,the detector-wall effect, and ballistic effects (incompletecharge integration, see [69] for a detailed discussion). In-formation on signal risetime can be used to eliminatesome of these artifacts [70], at the cost of lowering theefficiency.Nowadays, digital electronics allow a more detailedpulse shape analysis [71]or the use of the full responsefunction [72]. After parametrization of the detector re-sponse as a function of E n , several suitable algorithmscan be used to unfold the response from the measuredspectrum [20, 69]. The evaluation of systematic uncer-tainties in this method is not a simple task. Informationabout their magnitude can be obtained by comparison ofresults obtained by different groups and detector systems[20, 73]. This issue is discussed in Sect. III E.
2. Gaseous proton recoil spectrometers
This method is based on the detection of protons thatare elastically scattered by neutrons. The detectors usedare either methane- or hydrogen-filled proportional coun-ters at high pressure in which the gas acts at the sametime as the target for the reaction and as detecting me-dia. These detectors are insensitive to thermal neutronsand compared to He spectrometers have a better en-ergy resolution below ∼
200 keV. Because of this theyare considered to be superior in this energy range [31].They have, however, a lower efficiency which limits thepractical measurable energy range up to about 1 MeV.At typical β n energies, struck protons are scatteredisotropically and the ideal detector response is a stepfunction. Thus the neutron energy distribution is ob-tained by spectrum differentiation [74] rather than bydeconvolution [75]. Fourier filtering can be applied toreduce the fluctuations of the extracted distribution [76].However the true detector response departs from theideal response and a number of corrections must be ap-plied [17]. These type of detectors are sensitive to γ -rays that contaminate the low-energy part of the spec-trum ( <
100 keV), but γ signals are efficiently elimi-nated using pulse shape discrimination. Different dis-crimination methods have been applied [17, 77] and theenergy-dependent impact on neutron counting must beevaluated. In addition, the response is altered by the re-coils of heavier nuclei present in the gas mixture, by wall-and end effects and by position-dependent variations ofthe signal amplitude. The PSNS code [78] allows theinclusion of all these corrections and is commonly em-ployed to analyze the data. In general the corrections arefound to be small and sometimes instead of correctingthe data they are used to evaluate the size of the relatedsystematic uncertainties [17]. A comparison of the resultsobtained with this technique and with He spectrometersis presented in Sect. III E.
3. Neutron energy spectroscopy with time-of-flightspectrometers
The time-of-flight (TOF) methods involve detectionof neutrons using the β -neutron delayed coincidencemethod. In radioactive beam experiments, the start sig-nal for the neutron time-of-flight measurement is givenby a β detector trigger, and the stop signal is providedby a neutron detector, which is typically a fast plasticor liquid scintillator. The required time resolution forthe TOF measurements is in the nanosecond range. TheTOF distance and timing resolution determine the totalresolution [79].The key advantages of TOF arrays are the relativelyhigh intrinsic efficiency for high-energy neutrons, the abil-ity to measure neutrons without recording their full en-ergy, and the relatively well-understood interaction cross-sections with the scintillator which enables reliable simu-lations. The disadvantage of the TOF technique is thelimitation of the achievable resolution for high-energyneutrons ( > E ∼ /T OF dependencein the typical geometry and susceptibility of the detectorresponse to neutron scattering. Neutron- γ discrimina-tion can be achieved by using liquid scintillators. Thehigh cost of the detector material prevented the use ofsolid organic crystals such as stilbene and para-terphenylfor making large TOF arrays. Recently developed plasticscintillators with neutron- γ discrimination capability [80]are now available.Until recently the most successful TOF arrays used for β -delayed neutron spectroscopy were TONNERRE [81],which was used in experiments at CERN and at GANIL(France), and the TOF array developed at the NSCL(USA) [82]. Both were used to measure light-mass nu-clei with distinct neutron transitions [83–85]. The heavi-est studied isotopes were − K [86]. Both TOF arraysshare a similar design with about 1 m flight path, andlong and curved plastic scintillator bars.The currently operational TOF arrays for decay stud-ies are VANDLE [87, 88] (used at various facilities inthe USA, at CERN, and at RIKEN), DESCANT [89, 90]at TRIUMF/ISAC in Vancouver (Canada), and MON-STER which has been built for FAIR and already usedat ISOLDE and at the IGISOL facility in Jyv¨asky¨a [91].VANDLE is a TOF array using a fully digital data ac-quisition system [92]. The focus is on a high detectionefficiency with the use of straight bars made of EJ200plastic scintillators (Eljen Technology, USA). A digitaldistributed trigger enables a low-energy neutron thresh-old down to 100 keV.MONSTER is a TOF array based on BC501A (St.Gobain) and EJ301 (Eljen Technology) cylindrical liq-uid scintillators. Both BC501 and EJ301 offer excel-lent neutron/ γ -ray pulse shape discrimination capabili-ties, which allow to strongly suppress the competing γ -ray background and β -neutron detector coincidences dueto cosmic rays. MONSTER is operated with a fully dig-ital data acquisition system based on 14 bits resolution10evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al. and 1 Gsample/s digitisers.DESCANT is a 70-element array of deuterated liquid-scintillator detectors (BC-537, St. Gobain) that can beused with both the TIGRESS and GRIFFIN γ -ray spec-trometers at TRIUMF-ISAC for reaction studies and theinvestigation of β -delayed neutron emitters [89, 90]. DES-CANT forms a close-packed array that replaces the for-ward “lampshade” of 4 HPGe clover detectors in each ofthe GRIFFIN and TIGRESS γ -ray spectrometers, pro-viding high detection efficiency for neutrons in the rangeof ≈
100 keV to 10 MeV.The decay of N, a well-defined standard for neutron-branching ratio measurements (see Table I), can be usedfor energy- and detector-response calibrations in TOF ex-periments. The energy of the three main neutron lines arewell-known from He ion chamber measurements [93–97]and appear fully resolved in TOF measurements [81, 98].Alternatively, if a calibration with neutron transitionsof energies higher than 2 MeV is desired, the use of Bor K is possible. However, there are no high-resolution He-detector measurements for the decay of B, and onlyone measurement for K [99]. Several measurements ofthe delayed neutron emission of B [81, 82, 98] and K[86, 99] have been published using TOF arrays and showdeviations up to 10% in the reported neutron energies.Monte Carlo simulations are a complementary toolto calibrations since they offer a large flexibility andcan reach a high level of accuracy in the simulation ofneutron interactions and detector properties [100, 101].They are used for extending the overall efficiency cali-bration of a TOF spectrometer to a broader neutron en-ergy range than available with mono-energetic neutronsources. Moreover, Monte Carlo simulations can also beapplied for determining the time-energy relation of theneutron detectors, quantifying the cross-talk and estimat-ing the time-correlated neutron and γ -ray backgrounddue to elastic, inelastic and (n, γ ) reactions. Many newmeasurements have been performed in the past few yearsand the results are presently being analyzed. C. New methods (for P n values and energyspectra)
1. Total absorption γ -ray spectroscopy Total absorption γ -ray spectroscopy (TAGS) was firstapplied to β -decay studies at ISOLDE-CERN in the1970’s [102] as a tool to measure accurately β -decay in-tensity distributions. It has been used since then to tacklea variety of problems, including the investigation of reac-tor decay heat evolution [103], the nuclear level densitiesand γ -ray strength functions far from stability [104], andthe spectrum of reactor anti-neutrinos [105]. Recently itwas proposed to use this technique to measure P n val-ues and delayed neutron spectra [106]. This is indeed anexciting possibility, the current status of the method issummarized here. A total absorption spectrometer is a γ -ray calorimetermade with a large volume of inorganic scintillation ma-terial surrounding the source with a ∼ π solid-anglecoverage. Such a detector is capable of absorbing the fullenergy of the γ -cascade following the decay, thus identi-fying the excitation energy of the populated state. How-ever, due to detector inefficiency and β penetration, thisis not true for all events, and a spectrum deconvolutionprocedure is needed to recover the information.Due to the large detector size, neutrons emitted after β decay have a large probability to interact with the scin-tillation material through elastic collisions, inelastic scat-tering, and radiative capture. The latter two processesgenerate γ -rays that are easily detected. In principle, thisis a source of contamination of the spectrum that needsto be determined and subtracted [107].The neutron reaction cross sections, specific to the scin-tillation material, determine the amount of backgroundsignals. Large differences are observed in ( n, γ ) cross sec-tions between scintillators, which is the reason for thechoice of BaF in the spectrometer of Ref. [107] since theneutron-induced background is minimized.On the other hand, Ref. [106] proposes to turn thelarge capture cross section of NaI(Tl) into an advantage,allowing the measurement of neutron-emission probabili-ties and spectra. Beta-delayed neutrons captured in thescintillator produce a bump in the energy spectrum above ∼ . P n value.The difficulty of the method is that it relies on theMonte Carlo simulation of the transport and generationof radiation by neutrons in the detector to extract thedesired information [108]. Contrary to the simulation ofphoton transport, the accuracy of such simulations is notguaranteed a priori and should be investigated by com-parison between different codes and nuclear data libraries[100] and, if possible, by dedicated measurements [109].Alternatively, a collection of neutron emitters withwell-known P n values and neutron spectra can be mea-sured with TAGS and compared with the results of thestandard methods. This was done in Ref. [106] for thecase of I, and a good agreement was found with the P n value recommended in this CRP [36] (see Table I).However, in a similar work reported in Ref. [108], the P n value obtained for I was 11% smaller, while thevalue for Rb was found to be 22% larger than the eval-uation [36]. It is clear from this that further work isneeded, both experimentally and from the point of viewof simulations, to clarify the situation and establish thesystematic uncertainties of the method. This is worth theeffort – given the sizable number of β n emitters that havebeen measured recently and will be measured in the nearfuture with the TAGS technique.11evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
2. Ion-recoil methods
The Beta-decay Paul Trap (BPT) [110], an open-geometry linear radiofrequency quadrupole (RFQ) iontrap designed for precision β -decay studies, has been usedto determine β -delayed neutron ( β n) branching ratios andenergy spectra from the recoil energy imparted to thedaughter ions following β decay. This novel way to per-form β n spectroscopy circumvents the challenges associ-ated with direct neutron detection.The BPT collects and suspends radioactive ions in vac-uum at the center of a radiation-detector array consist-ing of ∆ E - E plastic scintillator telescopes, microchan-nel plate (MCP) detectors, and high-purity germanium(HPGe) detectors, used to detect the β particles, re-coiling daughter ions, and γ rays, respectively, emittedfollowing the decay. Following β decay, the recoil ionsemerge from the trap volume essentially unperturbed byscattering and the TOF of the recoiling ion to the MCPdetectors is determined. The β n decays can be identi-fied because the higher-energy recoil ions characteristicof neutron emission (with kinetic energies up to tens ofkeV) have shorter TOFs than the other recoiling daugh-ter ions (which have kinetic energies typically less than500 eV).The β n branching ratios can be deduced by comparingthe number of β -ion coincidences with TOFs character-istic of neutron emission to the total number of β decaysfrom trapped ions obtained from the number of detected:(1) β particles emitted from the trapped precursor, (2) β -ion coincidences with longer TOFs characteristic of β -decay to bound states, and (3) β -delayed γ rays.The agreement obtained for the β n branching ratioswhen using these three approaches provides additionalconfidence in the results. This approach was first demon-strated in Ref. [64] and has subsequently been used tostudy mass-separated ion beams of , , I, , Sb,and , Cs [111, 112] delivered by the CARIBU facilityat Argonne National Laboratory.Additional upgrades to the experimental setup can beimplemented to increase the solid angle of the detectorarray and to improve the ion collection and cooling whileminimizing the effect of the electric fields on the recoilions. Future experiments will also benefit from increasesin the intensity and purity of the low-energy beams de-livered by the CARIBU facility [113, 114].The recoil-ion approach is well suited to reconstructthe kinematics of a single undetected particle throughconservation of momentum and energy. The studies of β -delayed multi-neutron emission will need to incorporateauxiliary neutron detectors.
3. Optical Time Projection Chamber
The potential of using an optical Time ProjectionChamber (OTPC) to measure the neutron branching ra-tio via ion counting has been shown in [65]. The prin- ciple is the same as for the discovery of the two-protonradioactivity: a gas-filled TPC is used to produce ioniza-tion tracks of the incoming β n-precursor and the recoiling β n-daughter products which are then made visible via aCCD camera. Fig. 4 shows two different decay events ofthe β n emitter He. The picture shows only the incoming He nucleus and the recoiling Li, the β -delayed neutronis not visible. In the bottom of Fig. 4 the second decaypossibility of He into an α , a triton, and a neutron isshown.In principle one can reconstruct the energy of the emit-ted neutron from the length of the recoil tracks. This hasbeen done for the β -delayed triton decay of He via mea-surement of the momenta of the recoiling charged parti-cles ( α and triton) [115].The main limitation comes from the generally low re-coil energy and the finite resolution (diffusion effects)of the OTPC. So the technique is limited to low-massprecursors and reasonably high neutron energies. In thepresent setup with a gas mixture of 95% He and 5% N at atmospheric pressure, a lower threshold for neutronsof ≈ . P n values (and higher) since the energy reconstruction is notpossible with two outgoing (undetectable) neutrons. FIG. 4. (Top) β -delayed neutron decay of He into Li and aneutron (not visible) in the OTPC. (Bottom) β -delayed tritondecay of He into an α , a triton, and a neutron (not visible)in the OTPC. Pictures courtesy of Janas Zenon, University ofWarzaw/ Poland.
4. Measurement in a storage ring
The P n value could also be measured via ion countingin a heavy-ion storage ring. This complimentary methodhas been proposed for radioactive beams produced at the12evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
Fragment Separator (FRS) at the GSI Helmholtz Centerfor Heavy Ion Research in Darmstadt/ Germany whichare injected into the Experimental Storage Ring (ESR).Similarly, at the future Facility for Antiproton and IonResearch (FAIR) the β n-emitter will be produced at theSuper-FRS and injected into the Collector Ring (CR).While the β n-emitter is circulating in the ring and de-cays, the measurement of the neutron-branching ratiocould then be carried out via the ion counting method(see Sect. II A 8). This method has been described inRef. [66] but no proof-of-principle measurement has beencarried out yet.The advantage of this method is that symbiotically themass and/or half-life of the stored ion could be measurednon-destructively by time-resolved Schottky mass spec-trometry [116]. However, Schottky mass spectrometryrequires “cooling” to reduce the momentum spread ofthe beam. These beam cooling procedures take severalseconds and thus reduce the range of accessible β n pre-cursors.Capacitive Schottky pick-up plates provide the revolu-tion frequencies of the ions in the storage ring and allowtheir identification. When these ions decay, the changein mass and charge state leads to a change in the respec-tive revolution frequencies. With Schottky spectrometryit is only possible to study the daughter nuclei that re-main within the acceptance of the ring. This restrictsthe method in the ESR to parent-daughter pairs withinan A/q change of ± β − / β n-daughter nuclei.Like all described ion-counting methods this method isindependent of the energy of the emitted neutron and therespective neutron detection efficiency. However, differ-ent loss mechanisms during the storage in the ring needto be carefully addressed and investigated.The decay of the ions can occur anywhere on the ringorbit (which is ≈
108 m for the ESR at GSI Darmstadt)but only those decays that occur in the long straight sec-tions can be detected by a particle detector behind therespective dipole section. All other decays outside thissection will lead to a loss of the ions. For the ESR, amulti-purpose particle detector (CsISiPHOS) has beeninstalled and tested [117], which allows a geometrical ef-ficiency of ≈
5. Ion counting using a MR-TOF
Multi-Reflection Time-Of-Flight (MR-TOF) spectrom-eters are becoming more and more popular as devicesto measure precisely masses, determine the beam com-position, or to manipulate and clean ion beams. Thisversatility has also led to the proposal to measureneutron-branching ratios (including multi-neutron emis-sion branches) with a MR-TOF, parallel to the determi- nation of masses and half-lives [67, 119]. The setup at theFragment Separator (FRS) at GSI Darmstadt/ Germany,the so-called FRS Ion Catcher [120], consists of a Cryo-genic Stopping Cell (CSC) and a MR-TOF spectrometer.The composition of the fast (
E >
500 MeV/u) beam isidentified with the standard set of detectors at the FRS.A beam containing only the isotopes of interest is stoppedand stored in the CSC. After some decay time the ionsare then extracted from the CSC into the MR-TOF forfurther identification and measurement. The relative in-tensities of β n precursors and respective decay daughterswill then allow to extract the neutron-branching ratios.Fig. 5 gives a schematic view of the setup and a sim-ulated MR-TOF mass spectrum for the yet unmeasured β
2n decay of
Sb. Within the next years this promisingmethod will be tested with radioactive beams at the GSIHelmholtz Center in Darmstadt/ Germany.
FIG. 5. Schematic view of the MR-TOF techniqueusing a Fragment Separator (FRS), a Cryogenic Stop-ping Cell (CSC) and a MR-TOF device to count theions. At the bottom a simulated MR-TOF mass spec-trum is shown. Picture reprinted with permission from [67](https://creativecommons.org/licenses/by/4.0/).
D. Outlook for future measurements
There has been a lot of progress in measuring β n emit-ters in the last decade, especially with precision bet-ter than 5%. The earlier measurement campaigns weremainly driven by fission reactor studies and thus fo-cused around the two – low mass and high mass – fis-sion fragment groups. The reactor community still strivesfor more precise measurements of important fission frag-ments that are the main contributors to the delayed neu-tron yield ν d (see priority list on p. 15 in Ref. [40]) butthe general scientific focus has now shifted.The nuclear astrophysics community is interested inmeasurements of the most neutron-rich, heavy ( Z > N = 50, 82, and 126 shell closures which are the pro-genitor nuclei that are responsible for the creation of the13evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al. solar r -process abundance peaks at A ≈
80, 130, and 195.Masses, decay half-lives, neutron-capture cross sections,and neutron-branching ratios of these neutron-rich nu-clides are important nuclear physics input parameters forastrophysical network calculations, and in turn also helpto improve theoretical nuclear models that are requiredfor the prediction of even more exotic nuclei.A detailed review of the r -process nucleosynthesis, theastrophysical scenarios, the required nuclear data, howthey can be measured at radioactive beam facilities andwith what accuracy, is provided in Ref. [121]. Figs. 6 and7 give an overview of the status quo of β n-emitter as ofAugust 2020. These pictures include the vast amount ofmeasurements that were performed during the course ofthe evaluation work that has been published in Refs. [35,36] (see following Sect. III), as well as the majority of the(yet unpublished) data from the BRIKEN project [37, 51]which will conclude its campaign in 2021.This decade will see the transition to the new genera-tion of radioactive ion beam (RIB) facilities that are stillunder construction. Two of the main competitors for thestudy of the most neutron-rich β n-emitter will be the Fa-cility for Rare Isotope Beams (FRIB) at Michigan StateUniversity/ USA, which is planning to be operational bythe end of 2021, and the Facility for Antiproton and IonResearch (FAIR) in Darmstadt/ Germany which is aim-ing at producing the first beams in ≈ r -process experiments at these new facilities arethe so-called “Rare Earth Region” ( A = 160 − Z <
75 along the N = 126 shell closure.As can be seen in Fig. 7 and in the recently publishedevaluation [36], only a small number of β -delayed neu-tron emitters has been measured so far for Z >
57. Ex-periments in the next decade will allow us to access theseneutron-rich nuclei for the first time and achieve a betterunderstanding of the formation of these two abundancepeaks in the solar r -process abundance distribution. III. COMPILATION AND EVALUATIONA. Compilation and evaluation methodology
Standard procedures were followed for the evaluationof nuclear spectroscopic data as defined for the Evalu-ated Nuclear Structure Data File (ENSDF) and discussedat three Research Coordination meetings of the CRP[39, 40, 42], with the addition of guidelines for half-lifeevaluations as formulated by A.L. Nichols and B. Singh(see p. 31–40 in Ref. [122]). Emphasis has been placed onmaking sure that the P n value and half-life data have beencompiled thoroughly, together with the method used for each measurement, from all the available measurementspublished in peer-reviewed journals as well as in certainselected secondary references. This was followed by a se-lection of the most reliable set of data for a nuclide whichcould be averaged to obtain recommended values.Details of the procedures and policies of evaluationsfor this CRP are described in two publications. A de-tailed paper on the compilation and evaluation of datain the Z = 2 – 28 region (cut-off date December 2014)was published by M. Birch et al. [35] in 2015. The newlyevaluated data for Z = 29 – 83 (cut-off date August 2020)can be found in J. Liang et al. [36]. B. New evaluated ( T / , P n ) data In total, as of August 2020 data for nuclide identi-fication, half-lives and P n values have been extractedand evaluated for 653 neutron-rich known or potential β -delayed neutron emitters from more than 750 publica-tions, mostly in main-stream peer-reviewed journals.The evaluations in Refs. [35, 36] included only the veryfirst batch of data from the aforementioned BRIKENmeasuring campaign at RIKEN. The upcoming publica-tions will be included in evaluations of these mass rangesin the near future. The cut-off date for the data usedfor the calculations of macroscopic data in this CRP pa-per (see Secs. VI and VII) was March 2020. The dataused in these calculations can be found in the referencedatabase [43].Some data that was published in the months betweenMarch 2020 and the cut-off date of the Z >
28 evaluationwas included in the published version [36]. This data wasnot used for the calculation of macroscopic parametersin Secs. VI and VII as already mentioned, however, thedifferences are minute and have a negligible impact onthe calculated parameters.The most noteworthy addition is the inclusion of datapublished by the EURICA collaboration at RIKEN [123],measuring half-lives of 55 neutron-rich nuclei between
Sn and
La. In addition, for 13 neutron-rich nu-clei the β -decay half-life was measured for the first time: − Sb, − Te, − I, and
Xe. This led, forexample, to tiny changes in the recommended half-livesfor the P n standards , , Cs: • Cs: 581(6) ms −→ • Cs: 321.7(11) ms −→ • Cs: 229.7(10) ms −→ Z = 2 – 28 region Based on Q values deduced from the Atomic Mass Eval-uation (AME) 2016 for neutron-rich nuclides [33, 124], atotal of 221 experimentally observed nuclides were iden-tified as known or potential β -delayed neutron emitters14evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 6. Chart of nuclides for Z = 0 – 14 (top), Z = 15 – 28 (middle) and Z = 29 – 43 (bottom) with status for half-lifeand neutron-branching ratio measurements. Boxes show previously measured neutron-branching ratios, whereas circles indicateisotopes that have recently measured but have not yet been published or included in the latest evaluations [35, 36]. Crossesindicate isotopes for which half-lives have been measured for the first time recently. . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 7. Chart of nuclides for Z = 44 – 57 (top) and Z = 58 – 86 (bottom) with status for half-life and neutron-branching ratiomeasurements. Boxes show previously measured neutron-branching ratios, whereas circles indicate isotopes that have recentlymeasured but have not yet been published or included in the latest evaluations [35, 36]. Crosses indicate isotopes for whichhalf-lives have been measured for the first time recently. . . . NUCLEAR DATA SHEETS P. Dimitriou et al. in Ref. [35]. Of these nuclei, half-lives had been mea-sured for 180 nuclides, P n values for 114, P n values for21, and P n values for only three nuclides. There is onlyone nucleus, B, where a tentative P n value has beenreported [7]. In addition there were 9 isomeric values for P n values reported. For about 50% of the cases, P xn values are available from only one measurement.Since the cut-off date for this part of the evaluation wasin 2015, work on an update to include recent publicationshas started by the Canadian community. So far, fournew nuclides have been identified as β n-emitter , and twodecay half-lives and three new P n values were measured. Z = 29 – 57 region The latest evaluation comprised the heavier mass re-gion and was recently published [36] with a cut-off dateof August 2020. A total of 318 nuclei were identified as β -delayed neutron emitters, based on Q values deducedfrom the AME2016 [33, 124]. This region is of utmostimportance due to the production of most of these nu-clides in the fission of uranium and other actinides, andtherefore of relevance in nuclear power reactors. Out ofthese 318 nuclei, half-lives have been measured for 284nuclides, P n values for 183 nuclides, and P n values foronly eight nuclides. So far no P n or P n values have beendetermined in this mass region.The data for isomers are generally poorly determinedand often the half-lives and P n values are mixed withthe data for ground states. For a large number of cases P n values are available from only one measurement, andfor several others only upper limits are reported. How-ever the data for the main isotopes contributing to fissionyields seem to be in good order. Z = 58 – 87 region In this mass region 110 experimentally known nuclideswere identified as β -delayed neutron emitters based on Q values from the AME2016 [33, 124]. Half-lives areknown for only 54 of these, and P n values for only 9nuclides. Measurements for six Tl isotopes ( − Tl)and two Hg isotopes ( , Hg) were reported only re-cently [125, 126], while a tentative value of P n for Tlwas reported in a secondary publication in 1961 [34].
C. P n Standards
The selection of certain radionuclides as standards forP n follows criteria which are given in Refs. [35, 36]. Themain criteria for “good” standards are: • Easy production at various facilities (large quanti-ties, clean beams, no isomers). • Measured using reliable methods outlined inSect. II A in four or more independent experiments. • Consistent results with overall uncertainty of lessthan 5%.Exceptions are K, Ga, and , Cs, where the over-all uncertainty is 5–10%.
Cs has only three indepen-dent measurements, but these measurements are very ro-bust and consistent.In summary, the following nuclides are recommendedas P n standards, covering different Z regions up to Z =55: Li, C, N, K, Ga, Br, Br, Rb, Rb, I, Cs,
Cs, and
Cs. The recommended half-lives and P n values for these standards can be found inTable I. TABLE I. Table with P n standards and their correspondinghalf-lives as recommended from this CRP [35, 36].Nuclide Half-life (s) P n (%) Ref. Li 0.1782(4) 50.5(10) [35] C 0.7546(80) 99.28(12) [35] N 4.171(4) 95.1(7) [35] K 1.263(50) 86(9) [35] Ga 0.601(2) 22.7(20) [36] Br 55.64(15) 2.53(10) [36] Br 16.29(8) 6.72(27) [36] Rb 2.704(15) 10.39(22) [36] Rb 0.378(2) 8.8(4) [36]
I 24.59(10) 7.63(14) [36]
Cs 0.582(6) 13.5(6) [36]
Cs 0.3217(10) 14.3(8) [36]
Cs 0.2295(10) 28.5(20) [36]
D. Systematics for P n values In several studies [127–130] correlations between knownvalues of P n and other β decay gross properties ( T / , Q β , S n ) have been described to estimate unknown P n values. The basic correlation between P n and β -decayproperties is: P n = (cid:82) Q β S n S β ( E ) f ( Z, Q β − E ) dE (cid:82) Q β S β ( E ) f ( Z, Q β − E ) dE , (9)where S β ( E ) is the β -decay strength function and f ( Z, Q β − E ) is the Fermi integral. The integrations isperformed over the available β energy window, Q β − E .One of the earliest semi-empirical expressions origi-nates from Amiel et al. in 1970 [127]. Already then it wasknown that the neutron emission probability depends onthe available Q βn energy window, the level density, andthe competition of neutron and γ emission. A plot of thelog P n vs. log Q βn resulted in a linear dependence withslope m . This led to the conclusion that the dependency17evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al. of the P n value on the Q βn window is dominant over anyinfluence from the level density.The evaluated half-lives and P n values in this CRPwere analyzed by the three empirical approaches pro-posed by K.L. Kratz and G. Herrmann [128] (Kratz-Herrmann formula, KHF), an improved KHF system-atics developed by E.A. McCutchan et al. [129], and alevel-density dependent systematics by K. Miernik [130].These estimates can be used as guidance for future experi-ments close to the known region, as well as to cross-checkif outliers in existing data appear. They are howeverof limited use for r -process abundance calculations sincethey do not reach out far enough in A .For Z = 2 – 28 region, global fits with the Kratz-Herrmann and McCutchan et al. systematics were pre-sented in Ref. [35]. More detailed systematic plots usingall the three approaches are presented for the Z = 28 –57 region in Ref. [36], where a new approach of fitting theMcCutchan et al. systematics by individual Z has alsobeen presented for most of the elements in this region. Itappears that this approach has better potential for pre-dicting unknown P n values. Unfortunately, there is notenough data in the Z = 58 – 87 region to attempt fitswith the systematics.
1. Kratz-Herrmann formula
In the Kratz-Herrmann formula (KHF) [128] the β -strength function is assumed to be constant above a cer-tain cut-off energy C , and to be zero below that energy.It also assumes that the Fermi integral might evolve asa function of the Q βn value. This leads to the followingdescription: P n ∼ a (cid:18) Q βn Q β − C (cid:19) b , (10)where a and b are free parameters (fitted to the re-spective data range), and C is the cut-off parameter.The values for the cut-off parameter depend on the pro-ton/neutron number: • C = 0 for even-even nuclei. • C = 13 / √ A for even-odd/odd-even nuclei. • C = 26 / √ A for odd-odd nuclei.For the latest fit parameters and a log-log plot of P n asa function of (cid:16) Q βn Q β − C (cid:17) b , the reader is referred to Ref. [36].
2. McCutchan systematics
The considerable scatter and large reduced χ in theplots of the KHF systematics questions the reliability ofpredictions made employing this systematics. Thus, an improved systematics was developed by McCutchan et.al. [129] which considers both, the β -delayed neutronemission probability as well as the half-life. As the half-life is inversely proportional to the decay Q value, theratio P n / T / is considered as a function of the Q βn value: P n T / ∼ c Q dβn , (11)where c and d are fitted parameters.
3. Improved systematics along Z chains While the P n /T / systematics from McCutchan showan improvement over the KHF, there is still considerablescatter. ”Isotopic” systematics along a given Z can pro-vide a much better picture for unknown P n values. InRef. [36] this method was used for nuclides in the region Z = 29 −
57 which had three or more isotopes with ameasured value for their P n and T / , respectively.The improved systematics along a given Z shows linearbehavior when plotted in a log-log scale. Despite somescatter in this presentation, extreme outliers can indicateisotopes that require further investigation, e.g. the iso-topic chains of As, Pd, and Ba [36].
4. Systematics based on the Effective Density Model
The phenomenological effective level density functionmodel by Miernik [130] assumes that the β = strengthfunction is proportional to the level density ρ ( E ) fed by β -decay: S β ( E ) ∝ ρ ( E ) = exp( a d √ E ) E / (12)The parameter a d is fitted to existing data, so that thederived formula can be used across an entire mass surface.In order to calculate P n using this systematics, oneneeds to first find the a d for the nuclides of interest. Thenthe β -decay energy Q β of the parent and the neutronseparation energy S n can be used within the integrationof Eq. 9. The Fermi integral can be calculated preciselywith available tables, and the integration of Eq. 9 can becarried out numerically.An attempt to extend this model to multi-neutronemission (up to P n ) can be found in [131]. The assump-tion is that the neutrons are emitted sequentially, andthat the many-body channels are negligible. The limi-tation of this description is also that only Gamow-Tellertransitions are considered and that the neutron- γ com-petition is approximated with a ”threshold method”.Numerical values for the fit parameters and more de-tails are given in Refs. [36, 130].18evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
E. Delayed neutron spectra for individualprecursors
Delayed neutron spectra have been measured for lessthan 50 β n emitters. These include 34 fission productsfor which good quality data exists which was obtainedusing He and gaseous proton recoil spectrometers andmeasured by several groups at different installations. Asit was pointed out in the late 1970’s [19] discrepancieswere observed between the different sets of data in par-ticular at low neutron energies. This lead to an attemptto benchmark the different methods at different labora-tories [70] and triggered new measurements at other fa-cilities [17, 73].An evaluation of the available neutron spectra for the34 individual fission products was carried out during thethorough and comprehensive work presented in the PhDThesis of M. C. Brady in 1989 [31]. The list of isotopesincluded in the evaluation is given in Appendix D ofthat work. Most of the experimental data was comingfrom He spectrometer measurements carried out by theStudsvik group (G. Rudstam et al. ), the Mainz group(K.-L. Kratz et al. ) and the Pacific Northwest Labora-tory (PNL) group (P. Reeder et al. ). Proton recoil datafrom the Idaho National Engineering Laboratory (INEL)group (R. C. Greenwood et al. ) was also included. Addi-tional data was published by this group in 1997 [18] andthus was not included in the Brady evaluation.The data from the Studsvik group was provided withuncertainties. The uncertainty for the other data setswas inferred from generic assessments by the respectiveauthors. Brady [31] stated that the Mainz and Studsvikdata are in ”fair agreement” above few hundred keV, andare considered to be of better quality than PNL data.Probably because of this she gave preference to a singledata set instead of averaging different data sets, whenavailable.In general, due to the smaller uncertainties and broaderenergy range, preference was given to He data from theMainz group. If available, the proton recoil data fromINEL replaced the He data below 200 keV. The selecteddata were extended by theoretical model calculations tocover the full Q βn window. This procedure lead to arenormalization of the experimental data. The recom-mended data is presented in graphical form (figures 12 to45 in Ref. [31]).The originally evaluated data from Brady was incorpo-rated into the ENDF/B-VI decay data sub-library [132].Uncertainties are not included explicitly in the recom-mended data of [31] neither can they be retrieved fromENDF/B. In addition an evaluation of possible system-atic errors from the comparison of different data sets wasnot carried out in Brady’s work. The lack of realistic un-certainties for individual precursor spectra diminishes itshelpfulness. For example, it does not allow for an eval-uation of uncertainties on aggregate spectra calculatedby the summation method. In addition it is difficult todefine reference β -delayed neutron spectra for calibration or inter-comparison purposes. This issue is further dis-cussed below.
1. Digitization of delayed neutron (DN) energy spectra
Digitization of several β -delayed neutron spectra hasbeen done using the GSYS2.4.3 code and its later ver-sion 2.4.7 [133]. This code is routinely and extensivelyused for the digitization of cross section plots for the EX-FOR database [134]. The quality of the digitization waschecked by plotting the extracted data and comparingthe plot with the corresponding figure in the paper.The extracted datasets of all the figures were sent tothe IAEA Nuclear Data Section for further checking byan expert staff scientist. All the data files were finallyprepared for inclusion into the Reference Database fordelayed neutrons [43]. a. Z = 2 – 28 region: Beta-delayed neutron spectrafrom He [135], Li [136, 137], Li [5, 83, 138, 139], Be[138], B [81, 98], C [140], B [141], N [81, 98, 140], N [142], N [143, 144], and , Na [145] were digitized.Note that some of these are time-of-flight spectra, e.g. for Li from Ref. [136]. b. Z = 29 – 57 region: Spectra are available fromdifferent groups: • R.C. Greenwood and A.J. Caffrey [17]: Spectra ofdelayed neutrons for the isotope-separated, fissionproduct precursors − Rb and − Cs weredigitized independently by two groups over an en-ergy region of ≈
10 – 1300 keV. The data was trans-formed to an equidistant scale with an energy binof 1 keV for use in the summation method. • P.L. Reeder et al. [73]: Measured energy spectra ofdelayed neutrons from − Rb and
Cs were dig-itized. • M.C. Brady [31]: Several measured delayed neu-tron spectra obtained from different experimentalgroups (mainly Mainz, Studsvik, and groups atthe TRISTAN online separator) were analyzed inthis work as raw and adjusted spectra. This workincludes − Ga, As, − Rb, , In,
Sn,
Sb,
Te, − I, and − Cs. Both the rawas well as the adjusted spectra from this work weredigitized. • R.C. Greenwood and K.D. Watts [18]: Delayed neu-tron spectra of , , Br, − I, and
Te werepresented in this paper. All were digitized, and weresubsequently transformed to equidistant scale withan energy bin of 1 keV for use in the summationmethod.19evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al.
2. Assessment of spectra as a reference for calibrationpurposes
Defining β -delayed neutron reference spectra would bean important asset in practical work. These could serveto benchmark new setups and methods for the measure-ment of β -delayed neutron spectra. It will also serve tostudy the neutron energy dependency of the efficiency indevices aiming to determine neutron emission probabili-ties. The lack of an evaluation of uncertainties, in partic-ular systematic uncertainties, introduces ambiguities inthe results.An attempt was made within the CRP to asses thesize of systematic uncertainties by comparison of spectraldata obtained by different groups and different methods.However, it was realized that with the available informa-tion it is not possible to make a quantitative assessment.To illustrate the difficulty of the task, the cases of Rband Rb are shown in Fig. 8, which have reasonably large P n values and are easily produced in fission reactions.In the evaluation work of Brady [31], He spectrometerdata was available for both nuclei, provided directly bythe Mainz group and the Studsvik group. Data was avail-able also from the PNL group [73], but was disregardedbecause it had lower statistics and a smaller energy range.Preference was given to Mainz data over Studsvik datafor both isotopes, but no information is given about thedifferences between both data sets. Below 200 keV theMainz data was replaced by proton-recoil data from INEL[17].Figure 8 displays the resulting evaluated spectra as re-trieved from the ENDF/B-VII.1 library [24] (same spec-tra are available in ENDF/B-VIII.0 [25]). It is comparedwith the full INEL spectrum obtained by digitization ofthe graphical representation in [17]. The data from PNLis also included in the figure, and was obtained by dig-itization of figures in [73]. The three data sets are his-togramed with a 10 keV bin width and are normalizedto the counts in the region from 0.2 to 1.2 MeV. As canbe seen there are notable differences. When comparingvalues integrated over a range of 100 keV, to minimizethe effect of different energy resolution and statistics, thediscrepancies reach up to 30–50%. The drop observed inthe PNL data at around 0.5 MeV is likely due to a sud-den rise of their efficiency that the authors quote as ofuncertain origin but was also observed by other groups.Later this rise of efficiency has been identified as a spuri-ous effect of neutron resonances excited in iron which isgenerally present in the experimental setup [146].It is not easy to arrive to a conclusion regarding thesize of systematic errors from this information alone. Inparticular the loss of the primary information handledby Brady is unfortunate. In addition, it seems that thesystematic errors of the different techniques are not fullyunderstood. A proper evaluation work will require newwell-controlled measurements that should profit from theadvances in radioisotope production methods and instru-mentation made in recent years. [MeV] n E [ a . u .] n I Rb [MeV] n E [ a . u .] n I Rb FIG. 8. Comparison of measured β -delayed neutron spectrafor Rb (top panel) and Rb (bottom panel). Red line: Dataretrieved from ENDF/B-VII.1 database. Blue line: Data fromGreenwood et al. (INEL) [17]. Green line: Data from Reeder et al. (PNL) [73]
For practical applications the interested user should bewarned about possible large uncertainties in the shape of β -delayed neutron spectra retrieved from the ENDF/B-VIII.0 [25] and ENDF/B-VII.1 [24] libraries. Wheneverpossible the effect of spectra obtained from different mea-surements should be studied. It should be noted also thatthe experimental spectra in the ENDF/B data base areaugmented with model calculations to cover the full Q βn energy window. These calculations use FRDM+QRPA β -strength distributions [147] and Hauser-Feshbach neu-tron branching ratios [32] to obtain the neutron spectraas described in the following sections. The model spectraadditions are easily identified due to the smooth charac-ter of their distribution. IV. THEORY OF MICROSCOPIC DATA
In this section we compare the new evaluated CRP( T / , P n ) data described in Sect. III with “state-of-the-art” microscopic models. The comparisons are limitedto global self-consistent β -decay models that take into ac-count both the allowed Gamow-Teller (GT) and first for-bidden (FF) decays on equal footing and can be used tocalculate both half-lives and β -delayed neutron emissionprobabilities. Self-consistent models have the advantage20evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al. of being founded on first principles. Their parameters aredetermined from a limited set of sample nuclei and arethen kept unchanged for the whole nuclear chart. Thus,they are considered more reliable for extrapolations toextreme
N/Z ratios. However, before they are used forpredicting nuclear properties in unexplored mass regions,their accuracy has to be tested against existing exper-imental data. The aim of this section is to ascertainwhether these global models are robust in the descrip-tion of the evaluated CRP data which include new re-sults from ongoing large-scale experiments at RIB facili-ties worldwide. This will then mean they can be used inextrapolations to mass regions where experimental dataare either unavailable or inaccessible.Beta-decay properties are influenced by various differ-ent factors. First of all, the competition between theGT and high-energy FF transitions accelerates the β -decay, while in the region of the ground-state spin inver-sion such concurrence may produce isotopic irregularitiesin the half-lives and P n values. Second, the effects ofmany particle-many hole (np-nh) configurations substan-tially enriches and softens the β -decay strength distribu-tion. Third, a local fragmentation of the β -strength dueto deformation may change nuclear β -decay characteris-tics. In transitional nuclei a co-existence of spherical anddeformed shapes may also be of importance.In the comparisons, we use two self-consistent globalmodels which treat GT and FF transitions consis-tently, but do not take into account complex np-nh configurations or deformation effects. For com-pleteness we also include the results of the recentlyupdated microscopic-macroscopic model of Ref. [148]which are taken from the publicly available supplemen-tary tables ( https://t2.lanl.gov/nis/molleretal/publications/ADNDT-BETA-2018.html ).The three models are listed below: • Fayans Energy Density Functional (EDF) [149]combined with continuum quasiparticle random-phase approximation (CQRPA). A common abbre-viation DF+CQRPA is used below for different ver-sions of the density functional, namely DF3 from[150–152] as well as the extended DF3a which wasdeveloped within the CRP to compare with the newevaluated data. • Relativistic Hartree–Bogoliubov+QRPA [153]based on the D3C ∗ functional(RHB+RQRPA) [154]. This model was alsoextended within the CRP to perform globalcalculations. • Microscopic-macroscopic model of Ref. [148] basedon the latest version of the finite-range dropletmodel FRDM12 published in Ref. [155] combinedwith the BCS+RPA ‘(Q)RPA’ description for theGT decays and a phenomenological approach basedon the ‘Gross theory’ for first forbidden (FF) de-cays. The β -delayed neutron emission properties are estimated by considering the competition be-tween neutron and γ emission in the daughter nu-cleus using the Hauser-Feshbach statistical model(HF). This approach ‘FRDM12+(Q)RPA+HF’ isdifferent from the sharp cut-off model used in theprevious calculations [147] whereby multi- β -delayedneutron emission emission was assumed to occurat energies above the corresponding neutron sepa-ration.In addition to the above models, which are used in iso-topic chains and global comparisons of both T / and P xn values, we include the results from the finite amplitudemethod (FAM) [156] in selected comparisons of half-lives.The FAM is a mean-field model used up to now solely forcalculations of half-lives, however, it provides a break-through approach for treating deformed nuclei [157–159]with the Skyrme functional SkO’ [160], therefore is worthcomparing with the CRP data for deformed nuclei.A few attempts have been made to include complexnp-nh configurations within the self-consistent approachin the study of the fine structure of the β -decay strengthfunctions and integral β -decay properties. The preferredmodels are the latest versions of the interacting shell-model (SM) [161, 162] which include the allowed GTand FF decays. Also “beyond the QRPA approxima-tion” models based on the EDF approach have been de-veloped and applied to selected nuclei near the closedshells. Practical schemes of this kind of models are thephonon-phonon coupling model (PPC) within the FRSAapproximation [163–165] and particle-vibration couplingmodels (PVC) [166–168] of the β -decay strength function.However, these models are still limited to the allowed GTapproximation. Among the models with complex con-figurations, β -delayed neutron emission branching ra-tios have been tackled so far only in the SM frameworks[161, 162] and FRSA [164, 165]. We have included pub-lished results from the SM [161, 162], FRSA [163–165],and PVC models [166–168] in the comparison of half-lives of Ni in this report.Finally, we mention the self-consistent models forspherical and deformed nuclei in the GT approximation[169–174] which have been used in selected isotopic re-gions. Ref. [170] in particular is dedicated to the nextgeneration of JENDL evaluated decay data, including β -decay half-lives, β -delayed neutron branching ratios,as well as neutron energy spectra. A detailed reviewof the self-consistent models of β decay can be found inRefs. [175–177].Sect. IV A discusses the extensions to the two self-consistent models that were performed within the CRP.Comparisons of the models with the evaluated CRP( T / , P n ) data are shown in Sect. IV B for: (i) isotopicchains of nuclides in the fission mass region, (ii) isotopicchains of nuclides relevant to nuclear astrophysics and(iii) global comparisons with respect to the ( T / , P n )data and mass number A . Finally, theoretical DN spec-tra are compared with experimental spectra from Brady’sthesis [31] in Sect. IV E.21evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
A. Self-consistent QRPA-based models
The DF+CQRPA and RHB+QRPA models have beenextended to perform large-scale calculations of β -decayhalf-lives and delayed multi-neutron emission probabil-ities within the CRP. These extensions are briefly de-scribed in the following.
1. DF+CQRPA
The β -decay strength function is calculated in the ex-tended finite Fermi systems theory (FFST) [178] based onthe energy density functional (EDF) theory which allowsfor fully self-consistent description of the ground stateproperties of nuclei with pairing. Treating the effects ofmomentum and energy dependence of the functional andeffective forces on an equal footing leads one to the FayansEDF [149] with the fractional-linear dependence on nor-mal density. The surface and pairing components of theEDF contain the gradient of the density. Such an ansatzis more general than the standard density dependenceof the Skyrme functional that is a result of effective 3Ncorrelations. Within the present CRP the ground-stateand β -decay characteristics for more than 200 (quasi-)spherical nuclei were re-calculated with the DF3a func-tional [179] which differs from the previous version DF3by stronger effective tensor-like components. It gives thesame quality of description of the ground-state propertiesas the DF3 functional and a better description of β -decayof heavy nuclei [180].Based on such an approach a framework that allows forlarge-scale continuum QRPA calculations of the GT andFF β -decay properties (DF3a+CQRPA) was developedin Refs. [151, 152]. For large-scale β -decay calculationsthe effective approximation is used for the spin-isospin ef-fective NN interaction. In the one-particle-one-hole (ph)channel it consists of the Landau- Migdal interaction andone- π and ρ -meson exchange terms (modified for nuclearmedium effects). For nuclei with pairing correlations,the density-dependent, A -dependent, zero-range T = 1ground-state pairing is used. For the spin-isospin effec-tive NN interaction in the particle-particle (pp) channel(isoscalar T = 0 effective interaction or dynamic pairing)a mass-independent zero-range interaction with constantstrength is assumed.Allowed and first-forbidden transitions are treated onequal footing in terms of the full set of multipole oper-ators that depend on the space and spin variables. Therelativistic vector operator α and axial charge operators γ are reduced to their non-relativistic space-dependentcounter parts via the relations for conservation of vectorcurrent (CVC) and partial conservation of axial current(PCAC). An advantage of such a scheme is that it is con-venient to use in the full ph-basis continuum pnQRPAframework [151, 152].The correlations beyond the QRPA are included byre-scaling the spin-dependent multipole responses by the same energy-independent quenching factor Q =( g A /G A ) . The one-pion component of the residual inter-action is quenched by the same factor Q . The axial-vectorcoupling constant | g A /G A | = 1 . γ component ofthe spin-dipole operator is accounted for as in Ref. [181].The energy-dependent effect of np-nh configurations canbe included via the spreading width Γ ↓ [182].In the case of odd- A and odd-odd nuclei (hereaftercalled “odd” nuclei), their degenerate ground states aretreated through averaging the corresponding multipletcomponents via equal filling approximation. The interac-tion of the odd nucleon with a “core” and rearrangementeffects are properly taken into account [150].In 2016, the DF+CQRPA framework was extended byfixing the odd nucleon in a given state. In this way, theDF3a+CQRPA model can account for possible ground-state spin inversion effects which have been shown toimpact the β -decay observables [177, 183]. Though thepresent version of the model is basically limited by thespherical approximation, it should be noted that the de-formation caused by the unpaired nucleon is properlytaken into account in the FFST equations for the odd-odd and odd- A nuclei.
2. Relativistic Density Functional+QRPA
Large-scale calculations of β -decay half-lives and β -delayed neutron-emission probabilities were performed inRef. [153] with the main goal of applying the resultsin heavy-element nucleosynthesis and comparing themwith the new CRP ( T / , P n ) database. The model wasbased on the relativistic nuclear energy density func-tional (RNEDF), which constructs the nuclear groundstate from the nucleon mean-field and a minimal set ofexchange mesons together with the electromagnetic field.The ground-state properties were obtained from the rel-ativistic Hartree-Bogoliubov model which correctly de-scribes the pairing in open-shell nuclei. In the calculation,the D3C ∗ density functional, which includes momentum-dependent terms [154], was used together with the pairingpart of the Gogny D1S interaction for the description ofthe pairing correlations. For the isoscalar proton-neutron(pairing-like) NN-interaction, a two-Gaussian form wasused following its introduction in Ref. [184]. Unlike theDF+CQRPA approach, which is free from fitting the pa-rameters to the ‘output’ half-lives, the strength of theinteraction was adjusted to reproduce the experimentalhalf-lives available at the time.The FF transitions were treated at the same level asthe allowed GT transitions. The same value of the axial-vector coupling constant | g A /G A | = 1 . γ operator was not included. Forodd- A and odd-odd nuclei, the ground state energy wascomputed by constraining the average number of particlesto be odd which resulted in an even RHB state. Its energy22evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al. differs from the true
RHB state by the energy of the oddquasi-particle (or both in the case of odd-odd nuclei).This approach was tested on Q β -values for even- Z andodd- Z isotopic chains and was found to be in satisfactoryagreement with the data.The limitations of the model are: (i) the model con-siders nuclei to be spherical, disregarding the possibleeffects of deformation on the transition spectra, and (ii)the model determines the ground state and excitations atzero temperature which has implications for applicationsto the r -process nucleosynthesis since the latter takesplace at finite temperatures. Both approximations arenecessary to reduce the total computational cost of thelarge-scale calculations. B. Comparison with new evaluated ( T / , P n ) datafor important β -delayed neutron emitters The evaluated CRP ( T / , P n ) data described inSect. III are compared with the previously listed self-consistent global models [151, 153] and microscopic-macroscopic results [148] for light and heavy fission prod-ucts. The CRP data can be downloaded from the IAEAonline database [43]. The selected isotopic chains con-tain the most important β n-emitter associated with thehighest fission yields, as recommended by the evalu-ated libraries ENDF/B-VIII.0 [25], JEFF-3.1.1 [28] andJENDL/DDF-2015 [27]. In order to assess the quality ofthe description of the β -decay characteristics, we analyzeboth the T / and P xn values.
1. Light fission products a. Arsenic isotopes
The β -decay characteristics ofthe As isotopic chain ( Z = 33) are compared with thecalculations from the new DF3a functional within theDF3a+CQRPA model, as well as with the RHB+QRPA[153] and FRDM12+(Q)RPA+HF [148] models in Fig. 9.As can be seen in the figure, the DF3a+CQRPA calcu-lation in the GT approximation overestimates the eval-uated half-lives by up to a factor of 10. Inclusion ofthe FF decays and the experimental ground-state spin(J π = 5 / − ) leads to a slight underestimation (by up to19%) of the evaluated half-lives, while the RHB+QRPAand FRDM12+(Q)RPA result in an underestimation byup to a factor of 8. The deformation of As isotopes israther moderate and the quadrupole moments are esti-mated to be β ≈ . − .
15 [185]. The difference inthe results of spherical and deformed calculations of thehalf-lives is not significant.A sudden decrease of the P n value when crossing N =50 is correlated with the onset of the FF transitions. At N = 52, 53 a qualitative agreement is observed betweenDF3a+CQRPA and FRDM12+(Q)RPA+HF, though theexperimental P n values are up to a factor of 3 higher.However, the experimental data do not support a sharp increase of the P n value at N = 54 as seen in theFRDM12+(Q)RPA+HF and RHB+RQRPA models. b. Bromine isotopes The CRP half-lives and P n values for Br isotopes ( Z = 35, Fig. 9) are com-pared with results obtained from the DF3a+CQRPA andRHB+RQRPA models. Both frameworks show a be-havior that is typical of the dominance of the GT de-cays. The deformation in the Br isotopes is estimatedto be higher than in As isotopes ( | β | ≈ / given by thespherical DF3a+CQRPA and RHB+RQRPA are closerto the experimental data than those from the deformedFRDM12+(Q)RPA model. The latter underestimatesthe T / by up to a factor of 25 at A <
93 and shows asudden increase of T / at A = 94. At the same time, the N dependence of P n values in FRDM12+(Q)RPA+HFis in better agreement with the evaluated data, while theDF3a+CQRPA calculation describes the general trend ofexperimental half-lives and P n values.In Table II, the evaluated half-lives and P n values forBr isotopes are compared with those obtained from theDF3a+CQRPA (spherical option) and RHB+RQRPAmodels, as well as with the results from the FRDM+RPAmodel of Ref. [22] that uses the spherical GT approxima-tion (“QRPA-2”). The latter model (based on FRDM ofRef. [186]) was used to estimate the total (integral) DNyields in the evaluation of Wilson and England [187]. Fi-nally, the deformed FRDM12+(Q)RPA calculations thatinclude the FF decays within the Gross theory [148] arealso displayed.As can be seen in the table, DF3a+CQRPA describesthe general trend of the isotopic distribution of the half-lives and P n values for N <
58. It can be used for es-timating the total (integral) DN yield, as the cumulativefission yields of the DN emitters amplify the contributionof this region (see Sect. VI B 1). c. Molybdenum isotopes
The influence of deforma-tion on the β -decay properties is illustrated for the Moisotopes ( Z = 42) in Fig. 9. Here, β is ≈ − . < A <
118 while for A ≈
126 it is β ≈
0, as es-timated from the quadrupole moments [185].As can be seen from Fig. 9, the T / in Mo iso-topes obtained from the spherical DF3a+CQRPA andRHB+RQRPA model are in agreement with the CRPdata. They are also close to the results from the deformedFRDM12+(Q)RPA and FAM models in the N = 72 − β ≈ − .
35) for
N <
72, as well as in the (quasi-)spherical region
N > A -dependence of the half-lives inthe spherical models is quite smooth at N >
82. It shouldbe noted that a detailed study in Ref. [188] has shownsome sensitivity of the Mo half-lives due to the oblate,prolate or spherical shape. d. Rubidium isotopes
For the strongly deformed Rbisotopes ( Z = 37) with β ≈ .
35 [185], the sphericalRHB+RQRPA describes the experimental half-lives ex-23evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al. cept for − Rb but does not explain the P n valuesfor the important β -delayed neutron emitters , Rb(Fig. 9). The deformed FRDM12+(Q)RPA model tendsto underestimate the half-lives in the region of strong de-formation for − Rb, nevertheless it provides a gooddescription of the P n data.
2. Heavy fission products a. Iodine isotopes
In Fig. 9, the half-lives and P n values for the iodine chain ( Z = 53) are shown, includingthe important β -delayed neutron emitters − I whichare the main contributors to the total (integral) DN yieldsfor thermal neutron-induced fission of
U. The spheri-cal DF3a+CQRPA and the deformed FRDM12+(Q)RPAdescribe the half-lives reasonably for these moderately de-formed nuclei with β ≈ . − .
15 [185].As the FRDM+BCS+RPA framework adopted inRef. [148] does not retain the SO(8)-symmetry of theQRPA, it infers a notable spurious odd-even staggeringin half-lives and P n values. The RHB+RQRPA producesa very smooth N dependence and systematically under-estimates the half-lives but interestingly agrees best withthe experimental P n values.In the DF3a+CQRPA calculation two effects are im-portant: a ground-state spin inversion and contributionof the FF decays. The first one leads to a stabilization ofthe half-lives at N = 88 – 90 ( − I) and the secondinduces a reduction in the P n values. Notice that a sta-bilization of the half-lives of − I was observed in therecently published RIKEN data [189] (shown in Fig. 9and in Table II). b. Cesium isotopes
For the isotopic chain of the Cs β -delayed neutron emitters ( Z = 55, Fig. 9), the de-formation is β ≈ . − . T / at the beginning of the chain ( A = 141) where nuclei have a lower deformation.The evaluated half-lives at A ≈
150 indicate a kind ofplateau like the one observed in the iodine isotopes andin self-consistent calculations. The evaluated P n valuesat A >
146 also show a stabilization effect. This couldbe related to the ground-state spin inversion at
N > P n values the best yet underestimates the half-lives. On theother hand, the DF3a+CQRPA and FRDM12+(Q)RPAshow a behavior that reflects the competition of GT andFF decays in the region up to N = 92. For N >
A > P n values due to increasing con-tribution from the FF decays. Thus, for the I and Csisotopic chains, deformation is still not a decisive factorfor the mass dependence of the P n values. It can be seenthat for these isotopes the spherical approaches, namelyDF3a+CQRPA and RHB+RQRPA, provide a level of ac- curacy comparable to the highly parametrized deformedFRDM12+(Q)RPA framework.In Table II, the DF3a+CQRPA half-lives and P n val-ues for iodine isotopes are compared with the sphericaloption of the FRDM+RPA model (“QRPA-2”) [22] andthe recent deformed option of the FRDM12+(Q)RPA[148]. As can be seen, the FRDM+RPA, which was usedin the evaluation of Wilson and England [187] for estimat-ing the total (integral) DN yields, often overestimates theexperimental P n values. As it does not reproduce the ex-perimental half-lives, the corresponding isotopes are notcorrectly assigned to the I-VI group of the 6-group modelthat is used to describe the total (integral) DN activity(see Sect. IX for more on group constants).It can be concluded that for fission products a complexinterplay of many factors influences the β -decay prop-erties. The local fragmentation of the β strengths dueto deformation is not necessarily the main driving force.What is important is an appropriate description of theground-state properties: total energy release and single-particle energies. The competition of the GT and high-energy FF transitions, effects of complex np-nh configu-rations and possible ground-state spin inversion also havea strong impact on the results. In transitional nuclei, aco-existence of spherical and deformed shapes may alsoplay an important role.Summarizing, the self-consistent models give a ro-bust description of the β -decay properties of fissionproducts. The quality of description is comparable tothat of the highly-parametrized microscopic-macroscopicFRDM12+(Q)RPA+HF model. As it will be shown inthe next section, the self-consistent models are preferabledue to their predictive power. C. Comparison for isotopes relevant to nuclearastrophysics
In this section, the global models are compared withthe CRP ( T / , P n ) data for very neutron-rich isotopeswhich are at the edge of the current possibilities of on-going RIB experiments and yet are indispensable for themodeling of the r -process nucleosynthesis in nuclear as-trophysics.We focus on two reference semi-magic isotopic chains:Ni ( Z = 28, π f / orbital is filled) near the crossing ofthe neutron major shell N = 50 and Sn ( Z = 50, π g / orbital is filled) around N = 82. The reason for choosingthese isotopic chains is that β -decay properties of isotopesbefore and after the major neutron shell crossings offer asensitive test for nuclear structure models. The theoreti-cal results are compared with the available CRP data andthe half-lives from the latest RIKEN experiment [189].Throughout the comparisons we show that the massdependence of total half-lives and P xn is sensitive to astructural indicator % F F that represents the ratio of theFF (or GT) decays over the total rate:%
F F = λ FF /λ = ( T GT − T ) /T GT . (13)24evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
142 144 146 148 150 152020406080100 A P ( % ) A
142 144 146 148 150 1520.010.1110
FRDM12 + (Q)RPA DF3a + CQRPA RHB + RQRPA CRP
Cesium (Z=55) T ( s ) /
138 140 142 144 146 1480.010.1110
Df3a +CQRPA FRDM12 + (Q)RPA RHB + RQRPA CRP RIKEN 2020
Iodine (Z=53) A T ( s ) /
110 112 114 116 118 120 122 124 1260.010.11
CRP DF3a + CQRPA FRDM12 + (Q)RPA RHB + RQRPA FAM
Molybdenum (Z=42) A T ( s ) /
92 94 96 98 100 1020.010.1110100
Rubidium (Z=37)
CRP RHB+RQRPA FRDM12+(Q)RPA A T ( s ) / A
87 88 89 90 91 92 93 940.010.1110100
Bromine (Z=35)
CRP DF3 + CQRPA RHB + RQRPA FRDM12 + (Q)RPA T ( s ) /
84 85 86 87 880.1110
DF3a +CQRPA DF3a +CQRPA (GT only) FRDM12 +(Q)RPA. RHB + RQRPA CRP
Arsenic (Z=33) A T ( s ) /
84 85 86 87 88020406080100 A P ( % )
87 88 89 90 91 92 93 94020406080100 A P ( % )
92 94 96 98 100 102020406080100 A P ( % )
110 112 114 116 118 120 122 124 126020406080100 A P ( % )
138 140 142 144 146 148020406080100 A P ( % ) FIG. 9. (Left panels) Predictions for half-lives from various theoretical models for As, Br, Rb, Mo, I, and Cs isotopes comparedwith the evaluated CRP data. For − I also the latest RIKEN data from Ref. [189] is shown. (Right panels) Predictions for P n values for the same isotopes from various theoretical models compared with the evaluated CRP data. For more information,see text. . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
TABLE II. Evaluated and theoretical T / and P n values for bromine ( Z = 35) and iodine ( Z =55) isotopes. “FRDM+RPA” isthe model labelled “QRPA-2” in Ref. [22]. ∗ Latest data from Ref. [189].CRP evaluation DF3a (this work) FRDM + RPA [22] FRDM12 + (Q)RPA + HF [148] RHB + RQRPA [153] T / (s) P n (%) T / (s) P n (%) T / (s) P n (%) T / (s) P n (%) T / (s) P n (%) Br 55.64(15) 2.53(10) 47.730 0.99 37.25 1.129 6.543 0.0 3.407 5.3 Br 16.29(8) 6.72(27) 16.550 2.9 104.99 28.599 1.400 1.0 1.292 3.7 Br 4.338(22) 13.7(6) 6.290 12.6 10.76 41.746 0.177 1.0 0.597 7.8 Br 1.911(10) 25.6(15) 1.770 17.5 17.33 99.800 0.106 3.0 0.313 5.4 Br 0.544(10) 29.8(8) 0.980 18.5 0.762 73.365 0.051 9.0 0.175 15.8 Br 0.334(14) 33.1(25) 0.250 20.1 0.054 8.457 0.034 11.0 0.108 11.7 Br 0.152(8) 64(7) 0.120 33.4 0.221 100 0.040 27.0 0.072 48.5 Br 0.070(20) 30(10) 0.100 50.1 0.034 14.221 0.108 53.0 0.052 46.9
I 24.59(10) 7.63(14) 29.28 11.8 3365.424 98.980 18.099 3.0 0.948 5.5
I 6.251(31) 5.30(21) 5.1 1.5 9020.949 69.824 11.038 5.0 0.496 4.6
I 2.280(11) 9.74(33) 0.87 3.95 58.145 99.988 2.133 13.0 0.299 10.3
I 0.86(4) 7.88(43) 0.79 3.69 17.216 99.728 0.433 13.0 0.194 8.5
I 0.43(2) 21.2(30) 0.46 19.5 2.347 100 0.428 51.0 0.131 29.3
I 0.235(11) ∗ - 0.401 5.61 1.400 99.952 0.074 19.0 0.096 27.0 I 0.182(8) ∗ - 0.319 11.1 0.150 77.120 0.128 70.0 0.072 37.2 I 0.094(8) ∗ - 0.198 10.4 0.058 29.379 0.049 36.0 0.055 34.9 I 0.0897(93) ∗ - 0.126 61.9 - - 0.076 82.0 0.043 39.1 I 0.094(26) ∗ - 0.0762 62.7 - - 0.037 54.0 0.034 34.6 . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
Here, λ and λ FF are the total rate and rate of the FFtransitions only, respectively, T and T GT are the totalhalf-life and the half-life of the GT transitions only, re-spectively. Naturally, % F F reflects selection rules and,in particular, a reduction of the unique FF compared tothe non-unique FF. β -decay properties in the Ni region
For the reference doubly-magic nucleus Ni ( N = 50, Z = 28) and the isotopes in the region (both with Z < Z ≥ E x ) GT transitionsmostly define the total half-lives at N <
50, while theFF decays give less-important contribution to the total β -decay rates. Eventually, for nuclei with occupied pro-ton 1 f / orbital beyond the N = 50 neutron shell, thehigh transition-energy FF decays start to compete withthe GT decays, although the former continue to makea substantial contribution to the total half-life as theirtransition energies increase with N − Z .The total half-lives for the Ni chain obtainedfrom DF3a+CQRPA [151, 177], RHB+RQRPA [153],FRDM12+(Q)RPA [148], and FAM [157] are comparedwith evaluated data in Fig. 10. The FRDM12+(Q)RPAand DF3a+CQRPA results are close to the experimentaldata, though an odd-even staggering is observed in theFRDM12+(Q)RPA.For the spherical RHB+RQRPA as well as for the de-formed FAM, the deviation from the evaluated half-livesat N <
50 is quite pronounced. For the doubly-magic nu-cleus Ni, they predict 258 ms and 605 ms, respectively,compared to the experimental value of T / =122.2(51) ms[35, 191].In order to understand the origin of these deviations,it is necessary to analyze the contribution of the FF (orGT) decays to the total rate (% F F value, Fig. 10). For Niisotopes with neutron numbers N ≤
50, as the π f / or-bital is filled, the GT decays ( ν f / , π f / ), ( ν p / , / , π p / , / ) overwhelm the hindered FF-unique decay( ν g / , π f / ). Naturally, the % F F values obtainedfrom the DF3a+CQRPA for
A <
78 are low and thedrop of the %
F F values at A = 78 is mostly related tothe competition with the GT transitions. For the FAMand RHB+QRPA models, the calculated % F F values for A ≤
78 are higher by 30 and 50%, respectively. However,high %
F F values for
A <
78 are not supported by theselection rules and the available decay schemes.Thus, an overestimation of the half-lives for
A <
78 byRHB+RQRPA and FAM may stem from the predictedbalance between the GT and FF strengths. For
N >
50, the non-unique decays (2 d / , 2 s / → p / , / , f / )contribute to the decay process, yet the % F F values cal-culated from DF3a+CQRPA reach only 25% for A = 86,which is quite close to the FAM prediction. For A >
78, all calculations give similar half-lives although theRHB+QRPA gives different %
F F values.It turns out that the differences in the total Q β values,
72 74 76 78 80 82 84 86 8872 74 76 78 80 82 84 86 8810 -2 -1 Ni A % FF RHB+RQRPA FAM DF3+CQRPA FRDM+(Q)RPA CRP T / ( s ) Ni FIG. 10. a) (Upper panel) Half-lives for the Ni iso-topes ( Z = 28) calculated from DF3a+CQRPA (presentwork), RHB+RQRPA [153], FAM (even-even only) [157], andFRDM12+(Q)RPA [148] compared with the evaluated half-life data [35]; b) (Lower panel) Contributions of the first-forbidden transitions to the total decay rate (% F F value). multi-neutron emission thresholds, and quasi-particle lev-els predicted by the different models are very important.The different phase-(sub)-spaces defined by these quanti-ties are reflected in the β -strength distributions and aretranslated into the half-lives and delayed multi-neutronemission probabilities.The P xn for the Ni chain obtained fromthe DF3a+CQRPA, RHB+RQRPA, andFRDM12+(Q)RPA+HF models are compared in Fig. 11.It can be seen that in the RHB+RQRPA calculations,the peak of the one-neutron emission probability occursat Ni, two mass units earlier compared to the other twomodel calculations, and that the two-neutron emissionprobability mass behavior also differs. However, thethree experimental P n data points for − Ni are verynicely reproduced by the FRDM12+(Q)RPA+HF andthe RHB+RQRPA model, whereas the DF3a+CQRPAmodel seems to underpredict these isotopes.Finally, in Fig. 12 we compare the half-lives for theNi chain with the recently developed “beyond the pn-QRPA” models, such as the FRSA+PPC [163] whichtakes into account the phonon-phonon coupling, thePVA models with the particle-vibration coupling (PVC)[166, 167, 192], and the “quasi-particle time blocking ap-proximation” (QTBA) [168]. Hybrid shell-model resultsfrom [193] are also included in the figure.The calculations in Fig. 12 have been performed withinthe GT approximation which is more justified for
A <
78. In the pnQRPA+PVC developed in the recent pa-per [167], the experimental half-lives for the Ni isotopes27evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al.
72 74 76 78 80 82 84 86
72 74 76 78 80 82 84 86
72 74 76 78 80 82 84 86
DF3 + CQRPARHB +RQRPA P P P P P CRP P - P ( % ) FRDM12 + (Q)RPA P - P ( % ) P - P ( % ) A P P P P P CRP P P P P P CRP
FIG. 11. Delayed multi-neutron emission probabili-ties ( P n – P n ) for Ni ( Z = 28) isotopes calculatedwith FRDM12+(Q)RPA+HF [148], DF3a+CQRPA (presentwork), and RHB+RQRPA [153]. These models are comparedto the evaluated P n data for − Ni as published in Ref. [35]. are reasonably well described assuming a rather strong T = 0 pairing (except for A = 80). The correspond-ing 1p-1h QRPA calculation in the same framework hasgiven a factor of about 10-15 longer half-lives [167]. Thusthe renormalization due to the PVC turns out to be verystrong leading to QRPA+PVC half-lives that are only bya factor 1.5 shorter for Ni and by a factor 1.5 longer for Ni.A similar strong renormalization due to the PVC ef-fect is obtained in the QTBA approach [168]. Again,the pure pnQRPA half-lives obtained without assum-ing phonon-phonon coupling in the QTBA are muchhigher than the corresponding quantities obtained fromthe FRSA [165] which includes phonon-phonon coupling.Thus, the renormalization factor due to the effective in-teractions in these approaches differs significantly (byabout 1–2 orders of magnitude). Most probably this dif-ference is due to the fact that the QTBA model uses ex-perimental Q β values instead of self-consistently derivedones.The above discussion is important if one considers thepotential of these models: once the contribution of FFdecays is included, they could be implemented in globalcalculations of β -decay half-lives and β -delayed neutronbranching ratios. It has already been shown that “hy-
72 74 76 78 80 82 84 -2 -1 QTBA SM DF3+spread SM+FF FRSA-PPC HFB+QPVC CRP T / ( s ) A Ni FIG. 12. Half-lives for Ni isotopes calculated from QTBA[168], FRSA+QRPA+PPC [165] and HFB+QRPA+PVC[167] in comparison with with the evaluated data fromRef. [35]. Also shown are calculations from the SM [161],NuShellX [193] and DF3a+CQRPA with spreading [177]. brid” models, i.e. DF3a+CQRPA including the complexconfigurations through the spreading width [177] and theshell-model NuShellX with the FF decays added from theDF3a+CQRPA [193], can give an overall reasonable de-scription of the experimental half-lives in Ni for
A > N = 50 shell that was observed in the RIKENdata [191]. It is therefore reasonable to expect thatthe self-consistent ‘beyond pnQRPA’ models have thepotential to describe all these effects. In this respect,it is important to include the contribution of the first-forbidden decays in the present (spherical) ‘beyond pn-QRPA’ schemes.On the other hand, an effort to include the contribu-tion of the complex configurations into the deformed Fi-nite Amplitude Method (pnFAM) [157] would result ina universal approach that could be applied to the wholenuclear chart. β -decay properties in the Sn region
For the isotopes beyond the major neutron shell N =82 in the Sn region, the concurrence of GT and FFdecays has much in common with the Ni region. Weshow that the contribution of GT and FF transitions tothe β -decay rates differs for the Z <
50 and Z ≥
50 iso-topes. The intensive GT decays in the
Z <
50 nucleimostly correspond to the ( ν g / , π g / ) configuration.The high-energy GT decays contribute strongly to thetotal half-lives of the nuclei with Z <
N <
82. After28evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al. crossing the N = 82 neutron shell, the high-energy FFdecays which are mainly related to the ( ν h / , π g / )configuration are active. In contrast to what is observedin nuclei in the Z ≥
28 region, the high-energy GT transi-tions for
Z >
50 nuclei are hindered, as the p1 g / orbitalis blocked. At the same time, the high energy FF transi-tions ( ν f / , π g / ), ( ν f / , π d / ) come into effectand mostly define the total half-life.Fig. 13 shows the comparison of the half-livesobtained from DF3a+CQRPA, RHB+RQRPA,FRDM12+(Q)RPA, and FAM with the evaluatedCRP data. For completeness, we include Sn in theplot even though it is not a β n-emitter . Within theGT-only approximation, the DF3a half-lives are up toa factor 5 longer than the data. Taking into accountthe FF decays sets the balance between the GT and FFstrengths as shown in Fig. 14 and allows for an excellentdescription of the experimental half-lives for the Snisotopic chain.A rather high percentage of FF decays of 60–75% calcu-lated from the RHB+RQRPA may be the reason for thestrong underestimation of the half-lives of − Sn by afactor of 4–5. On the other hand the FRDM12+(Q)RPAhalf-lives overestimate the experimental data by a factorof ≈
132 134 136 138 140 P ( % ) A Tin
DF3a+CQRPA (GT+FF) DF3a +CQRPA (GT only) RHB+RQRPA FRDM12+(Q)RPA CRP T / ( s ) FIG. 13. Half-lives (upper panel) and P n values (lowerpanel) for Sn isotopes ( Z = 50). Calculated values fromDF3a+CQRPA [177], RHB+RQRPA [153], FAM [157], andFRDM12+(Q)RPA [148] are compared with the evaluated( T / , P n ) data. The half-life for Sn (no β n emitter,39.7(8) s) was taken from ENSDF. Note that for the reference doubly-magic nucleus
Snthe very low %
F F value predicted by DF3a+CQRPAcalculations (Fig. 14) is consistent with the decay scheme
132 134 136 138 140020406080100
Tin
DF3a + CQRPA FAM RHB+RQRPA % FF A FIG. 14. Contributions of the FF transitions to the to-tal decay rate (%
F F values) for Sn isotopes obtained fromDF3a+CQRPA (present work), RHB+RQRPA [153], andFAM [157]. observing 99% intensity for the decay to the GT state at1.325 MeV with a log( f t ) = 4 .
2. Accordingly, the DF3acalculates a half-life of 35.7 s, compared to the evaluatedvalue of 39.7(5) s from ENSDF. In contrast, the RHB+RQRPA predicts 610 s and the FAM a value of 820 s.The corresponding P n values (Fig. 13) obtained withRHB+RQRPA and DF3a+CQRPA agree in general withthe mass dependence of the % F F values predicted bythese models, however they underestimate the CRP datafor
A > P n values considerably which is consistentwith a gradually increasing share of the FF decays at N >
82 due to the increasing contribution of the ∆ J = 0g.s.-to-g.s. transitions at N = 83 −
86. The stabilizationof the P n values at N >
86 predicted by RHB+RQRPAand DF3a+CQRPA reflects a decrease of the %
F F val-ues for N = 87 −
90 ( − Sn) due to the competitionfrom the open high-transition energy GT decays.As was already mentioned, the β -decay characteris-tics of the semi-magic Ni and Sn isotopic chains arehighly sensitive to the details of the nuclear structureaspects of the models, in particular the energy-densityfunctional used. As we move further away from theclosed shells, these characteristics become less sensitiveto the details of the models. For example in the Pdand Cd isotopes that have pairing in both neutron andproton sectors there is good agreement between the self-consistent DF3a+CQRPA and RHB+RQRPA calcula-tions [153, 176, 177].To summarize, from the comparison of theory andevaluated data for a fairly broad range of nuclei shownin this section, the recommended theoretical approachis the quasiparticle random phase approximation (pn-29evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
QRPA) based on the energy density functional (EDF) ap-proach. Recently developed self-consistent models havebeen successfully used in this CRP to calculate the half-lives and β -delayed neutron rates of fission productsand nuclei near the major closed shells that are impor-tant for r -process modeling. Compared to the old semi-empirical models (“Gross theory” versions) and the semi-microscopic FRDM-based (Q)RPA framework for the GTdecays that is augmented by a statistical model for theFF decays, the self-consistent β -decay models have theobvious advantage of being well-founded on first princi-ples. By definition, the parameters of the self-consistentglobal models should be kept the same when extrapolat-ing to different mass regions across the nuclear chart.Global models based on the energy density functionalapproach are not only used in β -decay studies but also fora consistent description of a range of nuclear propertiesin a broad mass region, such as binding energies, radii,magnetic moments, fission barriers as well as nuclear re-sponses to different probes. Consequently, there is a widevariety of data available to constrain the EDF parame-ters and one can avoid using the “output” half-lives and P n values for such a purpose. Self-consistent global mod-els are thus a reliable and universal instrument for thedescription of the middle-heavy, heavy and superheavynuclei which are in the scope of the present paper.Finally, it is worth mentioning the rapidly developing“beyond the pnQRPA” models such as FRSA+phonon-phonon coupling [163, 164], the PVA models withparticle-vibration coupling [192] and the “quasi-particletime blocking approximation” (QTBA) [168]. These ap-proaches can potentially describe the β -decay strengthfunction over a wide range of masses across the nu-clear chart with a quality comparable to the multi-configurational shell-model. For example, the “suddenacceleration” of the β -decay after crossing the N = 50shell, that was recently discovered in the Ni isotopic chainat RIKEN [191], has been described by assuming np-nhconfigurations within the DF3a+CQRPA approach usingquasi-particle spreading. This confirms that such a phe-nomenon can only be explained by considering FF decaysand complex configurations simultaneously. D. Global comparisons of theoretical results
Global comparisons between the CRP evaluateddata and the self-consistent models DF3a+CQRPA,RHB+QRPA, as well as the microscopic-macroscopicmodel FRDM12+(Q)RPA(+HF) are presented in thissection. Large-scale calculations of the β -decay energyreleases ( Q β , Q βn ), half-lives ( T / ) and delayed neutron(DN) emission probabilities ( P n ) for hundreds or eventhousands of spherical, near-spherical and deformed nu-clei have been performed so far within several models.Nowadays these models provide a reliable data input forthe modeling of abundances in the astrophysical r pro-cess. They have also been used as predictions for the ongoing large-scale experimental campaigns at RIB facil-ities worldwide (see, e.g. Refs. [125, 189, 191, 194]).In Fig. 15, the ratio of half-lives and P n values fromFRDM12+(Q)RPA [148] and the evaluated data are plot-ted with respect to the evaluated values. It is obvi-ous that the half-lives and neutron-emission probabilitiesof almost all β n-emitter considered here are reproducedwithin one order of magnitude.In the case of half-lives, the majority is reproducedwithin a factor of two or better, denoted by the blackdashed lines. It is also noticeable that the scatter aroundthe ratio of 1 decreases with decreasing experimental half-life, which is a common pattern. Shorter half-lives arecharacterized by larger Q -values, and a larger portion ofthe decay strength is included within the Q β window.As a result the half-lives of shorter-lived nuclei are lesssensitive to the deviations of the model from the truestrength function.In the case of the comparison with experimental P n values in the bottom part of Fig. 15 several nuclei can befound aligned on diagonal lines. This surprising featureis due to theoretical P n values that appear only as inte-ger values in the FRDM12+(Q)RPA+HF model. Linesfor P n = 1,2,3,4, and 5% are shown in red to guide theeye. For cases where the experimental values are verysmall, e.g. lower than 1%, any deviation of the modelpredictions from the true energies and strengths of thetransitions will, as a consequence, result in relatively largedeviations of the total emission probabilities from the ob-served values.Figure 16 shows the same as Fig. 15, but for theo-retical results obtained using the RHB+RQRPA model[153] which was extended for nucleosynthesis calcula-tions and for use in comparisons in this CRP. Thegeneral behaviour of the model is quite similar to theFRDM12+(Q)RPA+HF shown above, but with some no-table differences. In the case of half-lives, the relativisticapproach manages to provide, on average, a somewhatbetter description for half-lives <
200 ms as indicated bythe smaller scatter of ratios around the value of 1. How-ever, for longer half-lives >
10 s the model seems to sys-tematically underestimate the experimental half-lives. Inthe case of neutron emission probabilities, the same diag-onal trend as for the FRDM12+(Q)RPA+HF model inFig. 15 can be seen, due to the fact that many nuclei havesimilar theoretical P n values around 1–2%.Figures 17 and 18 present the same results as in the pre-vious two figures, but now the ratios are plotted versusthe atomic mass number A , in order to explore the impactof shells on the results. The FRDM12+(Q)RPA+HF for-malism provides a very robust description of the data,without showing any visible strong dependence of themodel predictions on the atomic mass number (exceptfor a notable dip in the deformed A ≈ −
95 region).This is true both for the half-lives and for the one-neutronemission probabilities.However, the results obtained with the relativisticRHB+RQRPA model (Fig. 18) show significant effects30evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al. -3 -2 -1 FRDM12 + (Q)RPA + HF T / t heo / T / x p T (s) FRDM12 + (Q)RPA + HF P = 1% P t heo / P x p P (%) P = 5% FIG. 15. Ratios of theoretical and experimental results for the half-lives (upper panel) and P n values (lower panel) calculatedusing the FRDM12+(Q)RPA+HF formalism [148], plotted versus the corresponding experimental values. Diagonally alignednuclei in the lower plot are nuclei that have the same theoretical P n value. Lines for P n = 1, 2, 3, 4, and 5% are shown toguide the eye. of the nuclear shell structure on the quality of the re-sults in the description of the β -decay half-lives. Theseresults display a clear arch between two mass regions,from A ≈
90 to A ≈ β -decay half-lives are well reproducedwithin a factor of 2 (although longer than measured) forthe mass region A = 100 − Z = 25 −
35 and Z = 44 − T / ranging from 10 ms to 10 s. Thisconstraint is a consequence of the strength function for-malism which assumes that QRPA results are better forshort-lived nuclei with relatively large Q β energy window.Also, the limitation of the comparison to spherical andnear-spherical nuclei makes it easier to understand theorigin of the deviations from the experimental half-lives.Fig. 19 shows that most of the half-lives are in agreementwithin a factor of two with the evaluated data.In the lower panel of Fig. 19, the ratio of the theoret-ical and experimental half-lives are plotted as a functionof mass number A . The results indicate that the data isin general reproduced within a factor of 2 over the whole31evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al. -3 -2 -1 T / t heo / T / x p RHB+RQRPA T (s) P = 0.2% P = 1% RHB+RQRPA P t heo / P x p P (%) FIG. 16. Ratios of theoretical and experimental results for the half-lives (upper panel) and P n values (lower panel) calculatedusing the relativistic RHB+RQRPA formalism [153], plotted versus the corresponding experimental values. Diagonally alignednuclei in the lower plot are nuclei that have the same theoretical P n value. Lines for P n = 0.2 and 1% are shown to guide theeye. mass region, with no obvious discrepancies at shell clo-sures or for deformed nuclei around A ≈
85 and 120.In a number of cases, however, such as in K and Sbisotopes, the deviation has been shown to be related toground-state spin inversion rather than to deformation[177, 183].Similarly, the ratio of neutron emission probabilities of(near-)spherical nuclei is shown in Fig. 20 as a function of A . Overall, the experimental data are reproduced withinthe same factor of two. Again the exceptions to this trendare weakly deformed nuclei in the Z = 31 − A ≈ Z = 44 − A ≈
120 regions which have rather small P n values. In these cases, neglecting the spreading ofthe β strength due to deformation leads to a systematic underestimation of the P n values.It is worth stressing that the β -decay strength functioncan be modified by including the quasiparticle-phononcoupling. The sensitivity of the neutron emission prob-abilities to the strength distribution in the vicinity ofthe neutron emission thresholds S xn is extremely high.Consequently, in the one-particle-one-hole pnQRPA ap-proach, the accuracy of global predictions for the P n values is lower than for half-lives.In Fig. 21, the ratio of DF3a+CQRPA predictions toexperimental half-lives [125, 126] is shown for the heav-ier Os to Bi nuclei ( Z = 76–83). As one approaches the N = 126 shell closure, nuclei are either spherical or havea small ground-state deformation. For the bulk of the32evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
20 40 60 80 100 120 140 160 180 200 220 2400.010.1110100
FRDM12 + (Q)RPA + HF T / t heo / T / x p A
20 40 60 80 100 120 140 160 180 200 220 2400.010.1110100
FRDM12 + (Q)RPA + HF P t heo / P x p A FIG. 17. Ratios of theoretical and experimental results for the half-lives (upper panel) and total P n values (lower panel)calculated using the FRDM12 +(Q)RPA +HF formalism [148], plotted versus the atomic mass number. nuclei included in the DF3 calculations, we observe alarger spread of the half-lives of up to a factor of 5. ForHg isotopes around A = 210 with relatively low Q β val-ues, the DF3a+CQRPA underestimates the half-lives byone and RHB+RQRPA by two orders of magnitude, re-spectively (see Ref. [125]). Both DF3a+CQRPA andRHB+RQRPA underestimate the experimental half-lifeof Au [195, 196] by a factor of about 30 – 60.A comparison of the existing eight experimental P n values for nuclei beyond the N = 126 shell closure [125,196] is shown in Fig. 22. Note, however, that these are theheaviest nuclei for which P n values have been measuredso far. As can be seen, the experimental uncertainties arestill too large for any detailed comparison of the differentmodel performances.It is worth mentioning that global comparisons of β - decay half-lives have also been performed within the de-formed self-consistent QRPA model of Ref. [174]. Themodel uses the GT approximation and a global D1MGogny interaction. Only the half-lives of 145 sphericaland deformed even-even nuclei for which the experimen-tal half-lives are known were included in the comparison.The calculated ratio T theo / /T exp / is quite homogeneouswith respect to the mass number A and, more partic-ularly, the quadrupole deformation parameter β . Thetreatment of deformation reduces the overall deviationfrom the data to basically the same factor of 10 which wasobtained for spherical nuclei in Refs. [151, 153]. Includingdeformation in the model is therefore expected to lead toa marked improvement in the RHB+RQRPA half-livesfor deformed nuclei and similar levels of accuracy thatwere obtained for spherical nuclei in Refs. [151, 153].33evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
20 40 60 80 100 120 140 160 180 200 220 2400.010.1110100
RHB+RQRPA A T / t heo / T / x p
20 40 60 80 100 120 140 160 180 200 220 2400.010.1110100 P t heo / P x p A RHB+RQRPA
FIG. 18. Ratios of theoretical and experimental results for the half-lives (upper panel) and P n values (lower panel) calculatedusing the relativistic RHB+RQRPA formalism [153], plotted versus the atomic mass number. As far as the comparison of different microscopic mod-els with the CRP data is concerned, we observe that re-gardless of the treatment of deformation all models usinga concept of the β -decay strength function have difficultydescribing nuclei close to the valley of β stability withlow Q β values. The RHB+RQRPA calculations, for in-stance, tend to underestimate the half-lives for very heavynuclei, around A ≈
210 by more than an order of magni-tude [125, 126]. This generic feature is also true for themicroscopic-macroscopic model and “Gross theory”.Neutron-rich nuclei near the closed shells are the mainplayground for developments in the microscopic theories.The theoretical predictions of their β -decay properties –while being a crucial test for any nuclear structure theory– are also critical for planning experiments at RIB facil-ities. Additionally, these nuclei are also key for a betterunderstanding of the astrophysical r process. From the global comparisons we deduce thatDF3a+CQRPA [151], RHB+RQRPA [153], andFRDM+(Q)RPA(+HF) [148] models give overall acomparable description of the β -decay properties. Notethat a somewhat smaller spread in the DF3a+CQRPAhalf-life calculations (Fig. 19) with respect to theRHB+RQRPA (Fig. 18) is partially a result of thelimited comparison of (quasi-)spherical-only nuclei usedin the DF3a calculations. An important source ofdeviations from the experimental data may come fromthe description of the ground-state properties.In particular, the underestimation of the total decayphase-space Q β , as well as Q βxn sub-spaces may have adestructive impact on the predicted β -decay observables.This is especially true for the P xn -values, as these ob-servables are more sensitive to the different ”systematic”uncertainties of the theoretical strength functions.34evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
Z=18 - 55, T <10 s T (s) T / t heo / T / x p
40 60 80 100 120 140 1600.1110 T / t heo / T / x p A FIG. 19. Ratio of theoretical and experimental values of half-lives of (quasi-) spherical nuclei with Z = 18 − , −
35, and44 −
55, calculated using the DF3a+CQRPA formalism and plotted versus the evaluated experimental half-lives in the top paneland versus mass A in the bottom panel. Finally, with regards to the predictive power of themodels, if we consider the smaller number of parametersinvolved in the self-consistent models, as well as their uni-versality, we can conclude that the predictions of thesemodels are more reliable than those of the “Gross the-ory” and FRDM-based models whose parameters are de-termined near the stability line.
E. Delayed neutron spectra calculations
The microscopic-macroscopic approach described inthe previous sections was also used in the calculationsof delayed neutron (DN) spectra of fission products inRef. [32]. The FRDM95 [186] was combined with the(Q)RPA model [147, 198] to estimate β -strength func-tions which were then used as input in the Hauser-Feshbach statistical model (HF) to obtain DN branch-ing ratios and spectra. The HF calculations require sev-eral nuclear ingredients. For neutron and γ -ray transmis-sion coefficients, the Koning-Delaroche global optical po- tential [199] and the generalized Lorentzian E1 strengthfunction [200] were adopted, respectively, with a parame-ter set obtained from the Reference Input Parameter Li-brary (RIPL-2) [201]. For the nuclear level densities, theyused RIPL-2 for discrete levels and the Gilbert-Cameronlevel density formula [202] at high energies. Spin and par-ity selection rules for the decay of the precursor nuclei todaughter nuclei were observed.The microscopic-macroscopic approach(FRDM+(Q)RPA+HF) to calculating β -delayed neutronspectra is important for various applications as it canpredict the spectra for nuclei located on the neutron-richside of the nuclear chart for which experimental dataare not available. Furthermore, as has been discussedin Sect. IV, it provides an improved description of thedecay process leading to DN emission as it considersnuclear structure effects such as nuclear shell effects,level structures, and the spin-parity selection rules. The β -delayed neutron spectra calculated by [32] are nowadopted in the ENDF/B-VIII.-0 decay-data library [25].Within the CRP, we performed similar calculations of35evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
40 60 80 100 120 140 160 P t heo / P e x p A 0.01 0.1 1 10 1000.1110 P t heo / P n e x p P exp (%) Z=18 - 55, T <10 s
FIG. 20. Ratio of theoretical and experimental values of β -delayed one-neutron emission probabilities ( P n ) of (quasi-)sphericalnuclei with Z = 18 − , −
35 and 44 −
55, calculated using the DF3a+CQRPA formalism and plotted versus the evaluatedexperimental P n values in the top panel and the mass A in the bottom panel. DN spectra by using a Hartree-Fock-BCS model (SHF-BCS) – instead of the FRDM – combined with QRPAto obtain the β -decay properties. The DN emissionpart was calculated using the HF model [170]. Inthis SHFBCS+QRPA+HF model, the pairing correla-tion is treated by the BCS approximation with a zero-range volume-type force. The ground and excited stateswere self-consistently calculated with the SkO’ Skyrmeforce [203] in the cylindrical coordinate, where the ax-ial symmetry was assumed. A zero-range volume-typepairing was used in the pp-channel ( T = 0 pairing), andthe strength parameters were adjusted to obtain the bestpossible description of available half-life data for each iso-topic chain. Only allowed GT transitions are consideredin the β -decay channel in Ref. [170]. Odd-mass nucleiwere treated in the same way as the even-mass nuclei,and the blocking and polarization effects caused by cou-pling between valence particle(s) and core nuclei were not considered. The HF statistical model implemented in thecode CCONE [204] was used to calculate the competitionbetween DN and γ decays. The global neutron optical po-tential of Ref. [199] and enhanced generalized Lorentzian(EGLO) model [200, 205] were used to calculate the neu-tron and γ transmission coefficients, respectively. Forlevel densities, we used RIPL-3 [205] for discrete levelsand the formula of Gilbert and Cameron with Mengoni–Nakajima parameter set [206] for higher energies.Figure 23 shows the β -delayed neutron spec-tra obtained for Rb and Cs isotopes from SHF-BCS+QRPA+HF and FRDM+(Q)RPA+HF. The re-sults are compared with the evaluated data of ENDF/B-VIII.0 [25] and the experimental data obtained fromRef. [31] that were described in Sect. III E 1.For FRDM+(Q)RPA+HF, the β -delayed neutron spec-tra of Rb and
Cs deviate from experimental data,while those of Rb and , , Cs are reproduced ap-36evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al.
200 210 220 A T / t h / T / x p T / t h / T / x p T (s) Z= 76 - 83, T < 500 s
FIG. 21. Same as in Fig. 19 but for heavy ( Z = 76 −
83, Os to Bi) spherical isotopes calculated using the DF3a+CQRPAformalism [125, 126, 197]. The experimental data is taken from the recent evaluation [36]. P ( % ) DF3+CQRPA RHB+RQPA FRDM+(Q)RPA CRP
FIG. 22. Theoretical and experimental values for the β -delayed one-neutron emission probabilities of heavy (quasi-)spherical Hg and Tl isotopes ( Z = 80 , proximately. The SHFBCS+QRPA+HF model cannotdescribe the β -delayed neutron spectra of Rb and
Cs, while those of the other nuclei are approximately repro-duced. It is worth noting that some of the β -delayedneutron spectra are reproduced reasonably well by thesetheoretical models, even though QRPA approaches areunable to estimate the nuclear excited states within anuncertainty of a few hundreds keV. The deviations fromexperimental data are mainly attributed to the calculated β -strength function since both approaches use similar HFimplementations. For example, the β -delayed neutronspectrum of Cs is reasonably reproduced with SHF-BCS+QRPA+HF but not with FRDM+(Q)RPA+HF,which implies that the β -strength function of SHF-BCS+QRPA+HF is more suitable for this nucleus thanthe FRDM+(Q)RPA+HF strength function. This con-clusion is based on the assumption that the particle evap-oration process is correctly described.Similar systematic detailed comparisons of experimen-tal and calculated DN spectra that duly consider the un-certainties in the measured spectra and the ingredientsof the models are expected to lead to further improve-ments of the theoretical β -decay models in the future.However, as already mentioned in Sect. III E 1, it is stillnot clear how to quantify the experimental uncertaintiesin the measured spectra of Ref. [31], therefore, until thatis possible, caution should be exercised when comparingwith these experimental DN spectra.37evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
The published and digitized experimental DN spectraare available on the IAEA online database [43]. (a) Rb-94 DN S pe c t r u m ( M e V - ) Exp.ENDF/B-VIII.-0SHFBCS+QRPA+HFFRDM+(Q)RPA+HF 1 2 3 4 (b) Rb-95 DN S pe c t r u m ( M e V - ) (c) Cs-143 DN S pe c t r u m ( M e V - ) (d) Cs-144 DN S pe c t r u m ( M e V - ) (e) Cs-145 DN S pe c t r u m ( M e V - ) (f) Cs-146 DN S pe c t r u m ( M e V - ) DN Energy [MeV]
FIG. 23. β -delayed neutron spectra for , Rb and − Cs calculated with SHFBCS+QRPA+HF [170] andFRDM+(Q)RPA+HF [32]. The results are compared withexperimental data available in [31] and the evaluated spectrain ENDF/B-VIII.0 [24].
V. MACROSCOPIC DATA: METHODS ANDMEASUREMENTS
In the following sections we deal with macroscopicdelayed neutron data produced as a result of neutron-induced fission of major and minor actinides. These dataare of utmost importance for studies on kinetic responseand safe operation of fission reactors.
A. Methods
1. Total delayed neutron yields and time-dependentparameters
The direct methods used for measuring the macro-scopic delayed-neutron characteristics from neutron-induced fission of heavy elements are based on irradiat-ing the investigated sample by neutrons and subsequentlymeasuring the appropriate delayed-neutron observables:the time dependence of delayed-neutron activities or thedelayed-neutron energy spectrum. Neutron sources usedfor this purpose are mainly the neutron flux in nuclearreactors [207–214], critical assemblies [13, 215, 216], orelectrostatic accelerator-based nuclear reactions: Li(p,n),T(p,n), T(d,n), D(d,n) [217–223]. All experimental meth-ods are based on the assumption that the delayed-neutronactivity arising from the irradiation of the fissionablesample can be represented by the linear superpositionof the exponential decay modes, each with its own decayconstant dN ( t ) dt = A m (cid:88) i =1 (1 − e − λ i · t irr ) · a i · e − λ i · t , (14) A = (cid:15) n · σ f · φ · N f · ν d , where A is the saturation delayed-neutron activity, a i and λ i the relative abundance and decay constant of the i-thdelayed neutron group, respectively, t irr the irradiationtime, m the number of delayed neutron groups each ofwhich is associated with a group of delayed-neutron pre-cursors with similar decay constants, (cid:15) n the efficiency ofthe neutron detector, ν d the total delayed-neutron yieldper one fission, φ the neutron flux (1/cm s), σ f the fis-sion cross section (barn), N f the number of atoms in afissionable sample.A comprehensive study of the delayed-neutron emis-sion properties conducted by Keepin et al. [13] on Th, U, U, U, Pu, and
Pu lead to the devel-opment of a 6-group model of the temporary delayed-neutron characteristics ( a i , T i ), where T i = ln2/ λ i . Thismodel has been successfully used by the reactor commu-nity for many years. Only recently, an alternative 8-groupmodel based on a set of decay constants that are univer-sal for all fissioning systems was proposed and justifiedby Spriggs et al. [224, 225].In the case of instantaneous irradiation (prompt burst38evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al. irradiation, λ i t irr << dN ( t ) dt = A · t irr m (cid:88) i =1 λ i · a i · e − λ i · t . (15)From Eqs. (14) and (15) it becomes clear that the ac-curacy of the delayed-neutron parameters ν d and ( a i , T i )extracted from measured data depends to a large extenton parameters such as the accumulated statistics, the fis-sion rate in the sample R s = σ f · φ · N f , the transporta-tion time of the sample from the irradiation position to aneutron detector and the neutron background. The qual-ity of the obtained delayed-neutron data is also relatedto the incident neutron energy because the temporarydelayed-neutron parameters ( a i , T i ) are known to have anoticeable energy dependence when expressed in termsof the average half-life of delayed neutron precursors (cid:104) T (cid:105) ([226], [227]). a. Nuclear reactor-based methods. The most impor-tant advantage of the nuclear reactor-based method isthe high intensity of the neutron flux. With such a high-intensity flux it is possible to use very small samples offissionable nuclides (up to micrograms) as was demon-strated by Waldo et al. [207]. However, the long timeit takes to transport the sample in the reactor measure-ments does not allow one to resolve all 6 groups of delayedneutrons. Furthermore, given that the energy of the pri-mary neutrons can take a wide range of values or maybeis unspecified in many of the reactor experiments, it isnot straightforward to use these data in the evaluation ofdelayed-neutron parameters.As a rule, a single irradiation procedure is used in thenuclear reactor-based experiments. The time dependenceof the delayed neutron activity registered by a multichan-nel analyzer can be obtained by integration of Eq. (14)([222, 226]. (cid:90) t k +1 t k dN ( t ) dt dt = dN ( t k ) dt · ∆ t k = A · m (cid:88) i =1 (1 − e − λ i · t irr ) · a i λ i · (1 − e − λ i · ∆ t k ) · e − λ i · t k + B · ∆ t k , (16)where ( dN ( t k ) /dt ) · ∆ t k is the number of counts reg-istered in the time channel t k with width ∆ t k , B theintensity of neutron background. This decay curve isused to estimate the temporal delayed-neutron parame-ters ( a i , T i ), the saturation activity A , the intensity of thebackground B, and the covariance matrix of the estimatedparameters with the help of the least squares method(LSM). The obtained delayed-neutron decay curve, thevalues of the estimated parameters ( a i , T i ) and the back-ground B are used to calculate the total delayed neutronyield [212, 226, 228–230].One possible type of irradiation is the instantaneous(prompt burst) irradiation (see Eq. (15)). In this case, ameasured delayed-neutron decay curve can be obtained by the integration of Eq. (15) (cid:90) t k +1 t k dN ( t ) dt dt = dN ( t k ) dt · ∆ t k = A · t irr m (cid:88) i =1 a i · (1 − e − λ i · ∆ t k ) · e − λ i · t k + B · ∆ t k . (17)It is this type of irradiation that was used by Keepin et al. [13] for the measurement of the decay curves whichwere used for the estimation of short-lived group param-eters (from 3 through 6) and the determination of thetotal delayed neutron yield. The Godiva reactor (a barespherical U assembly) was used as neutron source. Inaddition, the total delayed-neutron yield was determinedwith the help of the following approximation [13]. t (cid:88) t dN ( t k ) dt · ∆ t k − B · ( t − t ) = A · t irr m (cid:88) i =1 a i · (cid:0) e − λ i · t − e − λ i · t (cid:1) = A · t irr m (cid:88) i =1 a i = ν d · (cid:15) · R s · t irr , (18)where t irr is the time of the neutron pulse, R s · t irr thetotal amount of fissions in a sample, and the sum of therelative abundances is equal to 1. b. Accelerator-based delayed neutron experiments. The neutron sources used in this method are the monoen-ergetic neutron fluxes from the accelerator-based nuclearreactions Li(p,n), T(p,n), T(d,n) He, D(d,n) He. Themain advantage of the accelerator-based method is thepossibility to investigate the energy dependence of de-layed neutron properties in a wide range of incident neu-tron energies from thermal to 20 MeV [217–223, 231].Eqs. (14) and (15) reflect one single cycle of measure-ment which includes the irradiation of the sample, the de-cay, and the counting of delayed-neutron activity. How-ever, in accelerator-based experiments a sample under-goes a number of cycles with the purpose of increasingthe statistics. The general equation for the determina-tion of the total delayed-neutron yields and temporaldelayed-neutron characteristics ( a i , T i ) on the basis of thedelayed-neutron decay curve accumulated during n cyclesis given by ([222], [232], [233], [226], [234], [230]) dN ( t k ) dt · ∆ t k = A · m (cid:88) i =1 T hi · a i λ i · (1 − e − λ i · ∆ t k ) · e − λ i · t k + B · ∆ t k , (19)39evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al. where T hi determines the history of irradiation T hi = (1 − e − λ i · t irr ) × (cid:32) n − e − λ i · T − e − λ i · T · (cid:18) − e − n · λ i · T (1 − e − λ i · T ) (cid:19)(cid:33) ,A = (cid:15) · σ f · φ · N f · ν d , with n the number of cycles, T the period of one cycle(irradiation, decay, counting, delay).This equation is used to estimate the values of the sat-uration activity A , the temporal delayed-neutron param-eters ( a i , T i ( i = 1 , ..., m )) and the background B on thebasis of the decay curves measured with different irra-diation times t irr . The A and B values and group pa-rameters of delayed neutrons are estimated using the it-erative least-squares method [226]. The decay curves ob-tained with short irradiation times were used to estimatethe parameters of the short-lived groups of delayed neu-trons, and the decay curves corresponding to long expo-sure times were used to estimate the parameters of long-lived groups. The result of the analyses of data from onerun of measurements comprising n -cycles of irradiationand counting is the set of the relative abundances of de-layed neutrons a i , the half-lives of their precursor T i , andthe covariance matrix of the group parameters [235]. c. Modulated accelerator beam technique. In delayedneutron measurements, a short irradiation time (seeEq. (15)) simplifies the interpretation of the experimen-tal data obtained in the total delayed yield measure-ments. This idea helped to develop an efficient methodfor the determination of the energy dependence of thetotal delayed-neutron yield from fission of several heavynuclei [217]. This technique is based on a modulatedneutron-source generated by a Cockcroft-Walton acceler-ator which utilizes the D(d,n) reaction for producing 3.1MeV and the T(d,n) reaction for 14.9 MeV neutrons. Fig-ure 24 shows the time sequences used for the modulatedneutron-source technique.
FIG. 24. Time sequences in the modulated neutron-sourcetechniques [217]. Delayed neutron counting is made in timeintervals ( T m − t c ). A long-counter neutron detector operating in anti-synchronism with the accelerator beam registers delayedneutrons in the time interval ( T m − t c ). Interpretationof the experimental data for this method is based on the equation for the non-cumulative DN decay curvemeasured after the n -th cycle of irradiation-counting se-quences dN ( t k ) dt · ∆ t k = A · m (cid:88) i =1 T hi · a i λ i · (1 − e − λ i · ∆ t k ) · e − λ i · t k + B · ∆ t k , (20) T hi = (1 − e − λ i · t irr ) · (cid:18) − e − n · λ i · T m − e − λ i · T m (cid:19) where the saturation activity is A = (cid:15) n · σ f · φ · N f · ν d ,and T m the modulation period. After reaching the equi-librium ( n → ∞ ) in the short time periodic irradiation( λ i T m <<
1) with the period of modulation T m , the sum-mation of delayed-neutron counts in the counting time( T m − t c ) can be expressed as follows: t (cid:88) t dN ( t k ) dt · ∆ t k − B · ( t − t ) = A · m (cid:88) i =1 (1 − e − λ i · t irr ) · a i λ i · ( e − λ i · t − e − λ i · t )(1 − e − λ i · T m ) = A · t irr T m − t c T m (21)where t is the time when the delayed-neutron count-ing t c starts, and t is the period of modulation T m (seeFig. 24). Another advantage of this method as comparedto the nuclear reactor neutron-source techniques is a min-imum of scattering and thermalizing material present inthe vicinity of the sample. The total delayed-neutronyield was measured from the fission of Th, U, U, U, and
Pu [217] nuclides. Later, Krick and Evans[218], using the same methodology, measured the totaldelayed-neutron yield as a function of the neutron energyfrom the fission of U, U, U, Pu, and
Pu inthe energy range 0.1 - 6.5 MeV. It should be noted thatthe on-beam arrangement of a neutron detector can leadto a degradation of its counting characteristics. Specialmeasures should be taken to find and eliminate this ef-fect (see paragraph devoted to measurements with theT(d,n) He neutron source). d. The neutron detector in delayed-neutron measure-ments.
The neutron detector most commonly used indelayed-neutron measurements is an assembly of He orboron counters distributed in a polyethylene or paraffinmoderator. A moderator allows one to shift the neu-tron energy to the region of high registration efficiency.The efficiency of the neutron detector is determined usingcalibrated neutron sources (Pu-Be, Am-Li,
Cf) or themonoenergetic neutrons produced from Li(p,n), D(d,n), V(p,n) nuclear reactions measured at a charged-particleaccelerator [236].40evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al.e. Fission rate determination in accelerator andreactor-based methods.
The main method used for thispurpose in nuclear reactor experiments is spectroscopy ofgamma rays emitted from fission products. Keepin et al. [13] determined the total number of fission in the samplesby standard counting of the 67 h β -activity from Mo.Benedetti et al. [211] determined the fission rate in thesamples by measuring the gamma activity of fission prod-ucts (
Ru, I, Ba/
La) that were induced in thesamples after irradiation. In the accelerator-based tech-nique, the fission rate in the sample is determined by mea-suring the neutron flux with the help of a fission chamberthat is placed in the immediate vicinity of the sample. Inthe modulated neutron-source method, the fission ratein the fissionable sample is determined by measuring thecount rates in two fission chambers sandwiching the sam-ple ([217], [218]). In the case of accelerator-based meth-ods with off-beam arrangement of the neutron detector ,the fission chambers are placed in front of and behind thesample along the beam line of the accelerator ([222],[228],[237], [229]). f. The effect of the concomitant neutron sourceD(d,n) He in delayed- neutron experiments with an accel-erator neutron source T(d,n) He.
In experiments usingthe T(d,n) He reaction as the neutron source, one hasto take into account the effect of a concomitant neutronsource which originates from the implantation of deuteronions in the backing of the tritium target. As the numberof implanted ions grows, the intensity of the concomi-tant neutron source D(d,n) He increases. This featureof the T(d,n) He reaction makes it difficult to interpretthe experimental data obtained in the respective experi-ments. A special method has been developed to measurethe intensity of the D(d,n) He neutron source in correla-tion with the ion charge accumulated on a tritium target[238]. This method allows one to account for the effectof the concomitant neutron source and has been usedin measurements of the relative abundances and periodsof delayed neutrons for neutron-induced fission of
Th, U, U, U, U, Pu,
Np, and
Am in theenergy range from 14 to 18 MeV. Details of the procedureare presented in ([238], [239]). g. The effect of degradation of the neutron detec-tor counting rate characteristic in an intense field ofhigh energy neutrons.
The delayed-neutron decay curverecorded in measurements of relative abundances and pe-riods of delayed neutrons from the fission of heavy nu-clides induced by neutrons from the T(d,n) He reactionwas found to undergo noticeable degradation in the firstseveral seconds after switching off the ion beam. A specialexperiment has been conducted to measure the countingproperty of the neutron detector after its irradiation byneutrons from the T(d,n) He reaction. In this experi-ment, the time dependence of the count rates from theAm-Li neutron source was measured immediately afterthe irradiation of the neutron detector by a T(d,n) Heneutron flux of different intensities in the energy range14-18 MeV. The obtained data were used to correct the measured decay curves of the delayed neutron activity inthe measurements of the relative abundances and peri-ods from fission of
Th, U, U, U, U, Pu,
Np, and
Am by neutrons in the energy range from14 to 18 MeV. Details of the procedure are presented in[239].
2. Delayed neutron integral spectra
There are two main methods used for the investiga-tion of integral delayed-neutron spectra. These are neu-tron spectrometry using He [240] and proton-recoil de-tectors [17, 18, 223] and the time-of-flight method [241].The time-of-flight method gives an excellent resolutionat low energy, however this resolution worsens rapidly atenergies above a few hundred keV. As an example, thefull width at half maximum (FWHM) of a TOF systemwith flight path 50 cm and time resolution 3 ns is 1.6,17.3, and 82.6 keV at energies 50, 300 and 900 keV, re-spectively. The proton-recoil spectrometer resembles thetime-of-flight method: the resolution is good at low ener-gies, while deteriorating at high energies. The full widthat half maximum of a proton-recoil spectrometer with 2.5atm of H for the same energies mentioned above, is 4.2,12.6 and 25.6, respectively. The He-spectrometer seemsto be the optimal tool over the whole energy range. Theresolution of this type of spectrometer is about 12-30 keVfor energies ranging from 10 keV to 3 MeV. A detaileddescription of the techniques used for measurements ofdelayed-neutron spectra including unfolding proceduresare given in a comprehensive review by Das [242]. Sincethe publication of this review, experimental work on com-posite delayed-neutron spectra has been carried out onlyat IPPE using an accelerator-based neutron beam [243].By applying the least-squares method to the compositespectra measured in several delayed time intervals follow-ing fission [244], one can unfold the group energy spectra χ i ( E n ). The main purpose of obtaining the experimen-tal group spectra is to use them to calculate the effectivefraction of delayed neutrons β eff [245]. B. New measurements and compilation
Since the last evaluation of macroscopic delayed-neutron parameters was performed in the framework ofWPEC-SG6 [14, 246], experimental activities related tomacroscopic delayed neutron data have mainly been car-ried out at IPPE (Obninsk). These activities have beendevoted to the measurement of the energy dependenceof the total delayed neutron yield and the relative abun-dances of delayed neutrons and half-lives of their pre-cursors for neutron-induced fission of
Th, U, U, U, U, Pu,
Np, and
Am in the energy rangefrom thermal to 18 MeV [226, 228–230]. In addition, theintegral energy spectra of delayed neutrons from ther-mal neutron-induced fission of
U have been measured41evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al. [243]. The relative abundances and half-lives of delayedneutrons from the relativistic proton-induced fission of
U have also been measured [247]. All the data re-lated to neutron-induced fission have been compiled inthe macroscopic section of the database developed by thisCRP [40] under the guidance of the Nuclear Data Section.The database is an extension of the summary of delayedneutron parameters by Spriggs and Campbell [248] andthe compilation by Tuttle [249] and comprises the to-tal delayed neutron yields, and the relative abundancesand half-lives of delayed neutrons in the 6- and 8-groupmodels with covariance and correlation data. The mainfeatures of the new IPPE macroscopic delayed-neutrondata and the earlier measured data are presented in thefollowing sections.
1. Energy dependence of the relative abundances andhalf-lives of delayed neutrons
The energy dependence of the relative abundances a i and half-lives T i of delayed neutrons have been mea-sured at the IPPE electrostatic accelerators for neutron-induced fission of Th, U, U, U, U, Pu,
Np, and
Am in the energy range from thermal to18 MeV. Monoenergetic neutron beams were generatedby means of the nuclear reactions T(p,n), D(d,n), T(d,n).The method used in these experiments is described inSection V A 1. Efforts were made to improve the exper-imental and data processing procedures by a) shorten-ing the transportation time, b) extending the delayed-neutron counting time, and c) averaging the temporaldelayed-neutron parameters obtained in different experi-mental runs to improve the accuracy of the delayed neu-tron temporal parameters ( a i , T i ). The IPPE measure-ments in the high energy range (14 – 18 MeV) revealedtwo plausible reasons for the large discrepancies observedin the delayed-neutron temporal parameters: (i) the dete-rioration of the counting efficiency of the neutron detectorin a high-intensity neutron flux and ii) the contaminationof the accelerator target by neutrons produced by theconcomitant D(d,n) He neutron source in measurementsusing the T(d,n) He reaction.The comparison of the delayed-neutron parameters( a i , T i ) obtained in the IPPE measurements with otherpublished data is shown in Figs. 25 and 26. The quan-tity that is compared is the average half-life (cid:104) T (cid:105) of thedelayed-neutron precursors introduced by Piksaikin etal. [227]. Since (cid:104) T (cid:105) is the combination of the delayedneutron parameters ( a i , T i ) obtained in the least-squaresfitting procedure and represents an average property ofthe system, it is not affected by the correlations which in-evitably exist between the delayed-neutron parameters.It should be noted that the (cid:104) T (cid:105) value depends neitheron whether one considers N as individual precursors ordelayed-neutron groups of precursors, nor on the timeboundaries of the delayed neutron groups.It can be seen from Figs. 25 and 26 that the average TABLE III. Results of the regression analysis of the energydependence (cid:104) T ( E n ) (cid:105) = A + B · E n .Isotope Intercept value A Slope value B(s) (s/MeV) U 12.63 ± ± U 9.04 ± ± U 8.08 ± ± U a ± ± Pu 10.54 ± ± a The energy range for analyses of
U data was 3.2-5 MeV. half-life of delayed-neutron precursors for all fissioningsystems under consideration decreases with increasing en-ergy of primary neutrons in the energy range from ther-mal to 5 MeV. The real scale of the variation in the rel-ative abundances and half-lives of delayed-neutrons canbe estimated in terms of the average half-life of delayed-neutron precursors with the help of the regression anal-ysis of the IPPE data shown in Fig. 27 for the ura-nium isotopes U, U, U, U and
Pu. Re-sults of the regression analysis of the energy dependence (cid:104) T ( E n ) (cid:105) = A + B · E n are presented in Table III.The temporal parameters of delayed neutrons pre-sented in this paragraph have been used in the evalua-tion of the relative abundances of delayed neutrons andhalf-lives of their precursors (see Section IX).
2. Energy dependence of total delayed neutron yield
The energy dependence of the total delayed-neutronyield from neutron-induced fission of
Th, U, U, U, U, Pu,
Np and
Am in the energy range0.3 – 5 MeV measured at the IPPE accelerator facility ispresented in Figs. 28 and 29.Most of the data have been obtained after the last rec-ommendations were made for the major nuclides U, U and
Pu [246]. The IPPE data are comparedwith both the earlier measured data and the evalu-ated data from the ENDF/B-VII.1 [24], JEFF-3.1.1 [28],and JENDL-4.0 [258] data libraries. The total delayed-neutron yields obtained on the basis of the systematicsand correlation properties of delayed neutrons ν d ( E n ) = a · (cid:104) T ( E n ) (cid:105) b [227] are also presented in Figs. 28 and 29.The IPPE data [227–230, 256, 257] are in agreementwith the corresponding data measured by Krick et al. [218] for target nuclides U, U, U and
Pu. Theenergy dependence of both sets of data for the nuclidesunder consideration is well reproduced by the data anal-ysis on the basis of the correlation properties of delayedneutrons ν d ( E n ) = a · (cid:104) T ( E n ) (cid:105) b at least in the energyrange up to 3-4 MeV [227]. According to the WPEC-SG6 recommendations [246] based mainly on the mea-surements of the effective delayed neutron fraction β eff at thermal and fast assemblies, the energy dependence ofthe total delayed-neutron yield for U and
Pu does42evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 25. The energy dependence of the average half-life of delayed-neutron precursors from neutron-induced fission of U, U, U, U. The references of the data can be taken from the compilation by Spriggs and Campbell [248] except for theIPPE data [226, 230, 235, 239, 250, 251]. not exceed 1%. The energy dependence of ν d in a 1 MeVinterval calculated on the basis of Krick’s data [218] showsthe following relative increase: U - 1.98% ( ± U - 0.52 % ( ± Pu - 2.06 % ( ± ν d ( E n ) = a · (cid:104) T ( E n ) (cid:105) b [227]. As canbe seen in the table both the experimental data and thedata obtained on the basis of the systematics show note-worthy energy dependence of the total delayed neutronyield. The difference between the thermal and fast energy ν d values obtained for U and
Pu by the summationcalculation on the basis of the JEFF-3.1.1 fission yielddata [28] is 24.5% and 21.2%, respectively [260].Thus, this strong indication of an energy dependenceof ν d for U, U, and
Pu observed in direct mea-surements is in contrast to the results obtained with helpof the β eff methods [246]. More work is needed to deter-mine the energy dependence of the total delayed neutronyields reliably. The most efficient and straightforward TABLE IV. Comparison of the energy dependence of the totaldelayed neutron yield from fission of U, U, Pu. dν d /ν d / et al. Keepin IPPE [227][218] [13] from ν d ( En ) = a · (cid:104) T ( En ) (cid:105) b U 1.98 ± ± U 0.52 ± ± Pu 2.06 ± ± way to do this is to conduct relative measurements withaccuracy ±
1% [261]. Apart from this, the reason why thesummation method gives such a large difference betweenthermal and fast ν d values also needs to be explored [260].43evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 26. The energy dependence of the average half-life of delayed-neutron precursors from neutron-induced fission of
Th,
Np,
Pu,
Am. The references of the data can be taken from the compilation by Spriggs and Campbell [248] except forthe IPPE data [226, 230, 232–234, 252–255].
3. Integral energy spectra of delayed neutrons from fissionof
U by thermal neutrons
A comprehensive analysis of the composite delayedneutron (DN) spectra measurements can be found in thereview by Das [242]. This review includes also the en-ergy spectra from individual precursors measured by [19],[15, 16] and [17, 18], and the spectra of 235 nuclides cal-culated with the help of the evaporation model. Recentlythe integral energy spectra were measured from the ep-ithermal neutron induced fission of
U at the IPPE ac-celerator based neutron beams. The measurements weremade to emphasize particular groups of delayed neutronprecursors using the high-resolution He-spectrometer ofFNS-1 type and applying different irradiation and count-ing time intervals. Two sets of measurements were per-formed. The first one was made with an irradiation timeinterval of 120 s, which was followed by measurements ofdelayed neutron spectra in a sequence of time intervalsas follows: 0.12-2 s, 2-12 s, 12-22 s, 22-32 s, and 32-152 s after the end of irradiation. The second set of mea-surements was made with an irradiation time interval of20 s and measurements of delayed neutron spectra in thetime intervals: 0.12-1 s, 1-2 s, 2-3 s, 3-4 s, and 4-44 s afterthe end of irradiation. About 3000 irradiation-countingcycles have been made within these measurements. Thetime sequence of irradiation and counting intervals usedmade it possible to consider some of the measured spec-tra as quasi-equilibrium. The comparison of these quasi-equilibrium spectra with the corresponding spectra fromother experiments are presented in Fig. 30.It can be seen from Fig. 30 that the IPPE [243] near-equilibrium spectrum has more pronounced peak struc-ture compared to the corresponding experimental dataobtained by other authors. The peak structure observedin the data of Evans et al. [240] is similar to the peakstructure of the IPPE data but the low-energy part ofthe spectra (below 300 keV) is about 30% lower thanboth the IPPE data and the data obtained by the sum-mation method using the microscopic spectra from indi-44evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 27. The energy dependence of the average half-lifeof delayed-neutron precursors from neutron-induced fissionof U, U, U, U and
Pu based on the datafrom IPPE [226, 230] and Keepin et al. [13]. The data ofMaksyutenko et al. [248] presented in Figs. 25-26 were notconsidered. vidual precursors. This could be explained by possibleerrors in the determination of the efficiency of the He-spectrometer or the correction that accounts for the neu-tron flux attenuation in the shielding used for rejectionof gamma rays [243]. Another important feature of thepresent near-equilibrium spectrum is the lower intensityof DN below 200 keV as compared to the earlier exper-iments with the exception of the data of Evans et al. [240]. Comparison of the IPPE integral energy spectrameasured at different time intervals after the end of theirradiation with the spectra calculated on the basis ofmicroscopic DN data is presented in Section VI C. Moredetails of the experimental procedure employed in theIPPE experiments can be found in [243].
4. ALDEN: new measurements of delayed neutron data
Apart from the experimental activities at IPPE (Ob-ninsk), recently new experiments have been conducted atthe Institut Laue-Langevin (ILL) to measure aggregatedelayed-neutron data. The ALDEN (Average Lifetime ofDElayed Neutrons) project consists of a series of experi-ments designed to measure delayed neutron group abun-dances with the aim of improving the data and provid-ing realistic uncertainties and correlations for the mostimportant fissioning systems involved in reactor applica-tions ( U, U, Pu,
Pu) [262].The first experimental campaign of ALDEN was heldat the end of 2018 at ILL (Institut Laue-Langevin) [262].The ILL reactor produces a very intense and well-characterized thermal neutron flux. The experiment con-sisted of irradiating the fissile target and letting it decaynaturally. Delayed neutrons were measured by LOENIE,a He detector, optimally designed to have an efficiency that is independent of the incident neutron energy [262].LOENIE is composed of a cylindrical polyethylene blockwith a central hole for the fissile material and 16 smallerholes for the He counters. An airtight fission chambercontaining a deposit of fissile material was used as targetin the experiment. With the fission chamber one esti-mates the fission rate during the irradiation phase, whichis then used to normalize the delayed-neutron activitycurve.During the decay phase, the He counters registerdelayed neutrons as a function of time. This time-dependent activity curve was used to derive the groupsabundances in the 8-group model. Several irradiationcycles were performed, each with a different irradiationduration in order to saturate a specific group of precur-sors.The result obtained for thermal neutron-induced fissionof
U from this first experimental campaign in 2018 iscompared with other experimental data and evaluatedlibraries in Fig. 31. More ALDEN measurements for theother major actinides are planned to take place in thenear future.
C. Estimation of energy dependence of totaldelayed neutron yields
As discussed in Section V B 2, the incident-energy de-pendence of the total delayed neutron yield has been mea-sured extensively by the IPPE group in the past twentyyears [222, 228–230, 236]. On the other hand, the theoret-ical study of the energy-dependence of the total delayedneutron yield has not been pursued that actively. Theevaluated libraries, such as ENDF/B-VIII [25], JEFF-3.1.1 [28] and JENDL-4.0 [258], either perform an inter-polation of the existing data or use the systematics pro-posed by Tuttle [263], Benedetti [211], Waldo [207], andManero [264]. As a result, the evaluated values lie on astructureless curve.The dependence of total delayed neutron yields on theincident neutron energy results from two factors. One isthe dependence of fission product yields on the incidentneutron energy. Fission yield distributions are usuallydetermined by the potential energy surface of fissioningnuclei, which varies with incident neutron energy and ex-citation energy of the compound nuclei. The other factoris the competition with open channels other than ( n, f ).In particular, ( n, n (cid:48) f ) and ( n, nf ) channels have a largeimpact on the energy dependence of the total delayedneutron yields. Similarly, other channels accompanyingmultiple particle emissions like ( n, nf ) also affect theenergy dependence of delayed neutron emission.In Ref. [265], a new method for evaluating the inci-dent neutron energy dependence of total delayed neutronyields using least square fitting was presented. The modeladopted the incident neutron energy dependence of fissionproduct yields, the multi-chance fission, and the evalu-ated decay data of Ref. [35] ( Z = 2 – 28). As mentioned45evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 28. The energy dependence of the total delayed-neutron yield from neutron induced fission of U, U, U, U. Thereferences can be taken from the evaluation by Tuttle [249] except for the IPPE data by Piksaikin et al. [227, 228, 230, 256, 257]and Roshchenko et al. [229]. in Section III, new evaluated ( T / , P n data for Z > Z p isexpressed by the following equations; Z p ( A, E n ) = αZ p ( A ) + βc ( A ) E n + γE n . (22)The function c ( A ) accounts for the fact that the energydependence of Z p changes smoothly for light fragmentsand relatively rapidly for heavy fragments [266, 267]. Theparameter Z p ( A ) is taken from the evaluation of Englandand Rider [268].To take into account the odd-even effect observed infission yield distributions, the method proposed by Mad-land and England [269] was adopted, where (1 + C ),(1 − C ), (1 − C ), and (1 + C ) are multiplied by thefission yields of even-even, odd-odd, odd-even, and even- odd nuclei, respectively. The renormalization is carriedout after applying the multiplication factors. The energydependence of the odd-even effect is approximated as C k ( E n ) = C k
21 + exp ( ξE n ) (23)where C k ( k = 1 ,
2) are taken from Madland and Eng-land’s evaluation [269]. The values of α, β , γ in Eq. (22)and ξ in Eq. (23) are determined by a least squares fit-ting to experimental data on total delayed neutron yieldsfor , , , U and − Pu. More details about themethod can be found in Ref. [265].For , , Pu, the parameter γ was set equal to zerobecause there are not enough available experimental datapoints for all the parameters to be determined uniquely.The least square fitting was thus performed only for α, β ,and ξ for the above-mentioned actinides. The parame-ters obtained from fitting the new evaluated CRP dataare listed in Table V, The differences observed betweenthe values in this table and those in Table 3 of [265] re-46evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 29. The energy dependence of the total delayed-neutron yield from neutron-induced fission of
Th,
Np,
Pu,
Am.The references can be taken from the evaluation by Tuttle [249] except for the IPPE data of Piksaikin et al. [227, 230, 256,257, 259]. flect the impact of the new evaluated CRP data ( T / , P n )from Section III. It should be noted that in this work, thetotal delayed neutron yield of U (i.e. from U( n, f ))taken from JENDL-4.0 is multiplied by a factor of 1.2.This increase improves the results obtained for the de-layed neutron yields of U and
U at energies wherethe second-chance fission U( n, n (cid:48) f ) or the third-chancefission U( n, nf ) occurs. This prescription is validatedby the large ambiguity affecting the original total delayedneutron yield value of U of JENDL-4.0 as it is obtainedfrom Tuttle’s systematics [263].The total delayed neutron yields for uranium isotopesof A = 233 , , ,
238 are shown in Fig. 32 togetherwith the experimental data and the evaluated valuesfrom JENDL-4.0 [258], ENDF/B-VII.1 [24] and JEFF-3.1.1 [28] libraries. The energy dependence of the exper-imental data for , , , U is reproduced reasonablywell with the new parameterization.The present results agree roughly with the evaluateddata, however, several differences are noted: First, the
TABLE V. Parameters determined by the least square fittingto the experimental data.Nuclide α β γ ξ
U-233 1 . . − . × − . . . − . × − . . − .
195 1 . × − . . − .
922 4 . × − . . − .
010 6 . × − . . .
326 0 0 . . .
794 0 0 . . .
414 0 1 . new results give a smooth curve up to about 4 MeV,while the evaluated data give a straight line. Second,they are systematically higher than the evaluated data inthe energy region from 8 to 10 MeV. At energies above15 MeV, the new results are lower than the evaluateddata for , U. At these high energies, measurements47evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 30. Quasi-equilibrium spectrum of delayed neutronsfrom the fission of
U by epi-thermal neutrons [243]. INIPPE spectrum (1): counting time is 1.88 s after irradiationof 120 s. In IPPE spectrum (2): counting time is 0.88 s afterirradiation of 20 s. Quasi-equilibrium spectra by other au-thors have been calculated with the help of the group spectraobtained by decomposition of appropriate aggregate spectrain different time windows. The data references can be foundin the review of Das [242]. n (MeV) ν d ( n e u t r o n s / f i ss i o n s ) ENDF/B-VII.1JEFF-3.1.2JENDL-4.0Krick, Evans, 1970Clifford, 1972Cox, 1974Synetos, 1979 Keepin, 1957Conant, 1971Besant, 1977Loaiza, 1998Piksaikin, 1999Piksaikin, 1997 (absolute value)Foligno, 2019
FIG. 31. The energy dependence of the total delayed-neutronyield from neutron induced fission of
U. The red crosscomes from the 2018 ALDEN campaign [262]. The other ex-perimental data are taken from the evaluation of Tuttle [249]except for the IPPE data which are from by Piksaikin et al. [256, 257]. of total delayed neutron yields are required to improvethe evaluated data.Figure 33 shows the total delayed neutron yields forplutonium isotopes of A = 239 , , , Pu. However, thereare fewer available experimental data for the plutoniumisotopes , , Pu compared to the uranium isotopes.As in the case of the uranium isotopes, measurementsof total delayed neutron yields at energies close to thesecond-chance fission threshold are required, in order tomake a reliable extrapolation up to 20 MeV.
U-233 ν d ( neu t r on / f i ss i on s ) This WorkJENDL-4.0ENDF/B-VII.1,JEFF-3.2Keepin,1957Brunso,1955Masters,1969Conant,1971Rose,1957Notea,1969Piksaikin,2006,2013Krick,1970
U-235 ν d ( neu t r on / f i ss i on s ) This WorkJENDL-4.0ENDF/B-VII.1JEFF-3.2Piksaikin,1999 (absolute value)Krick,1970Clifford,1972Cox,1974Synetos,1979Piksaikin,1999
U-235 ν d ( neu t r on / f i ss i on s ) Masters,1969Besan,1977Keepin,1957Conant,1971Loaiza,1998
U-236 ν d ( neu t r on / f i ss i on s ) This WorkJENDL-4.0ENDF/B-VII.1JEFF-3.2Bobkov,1989Brady,1989Tuttle,1979Gudkov,1989Roshchenko,2006; Piksaikin,2013
U-238 ν d ( neu t r on / f i ss i on s ) E n (MeV) This WorkJENDL-4.0ENDF/B-VII.1JEFF-3.2Keepin,1957,1969Rose,1957Cox,1970Cox,1974Besant,1977Brunson,1955
U-238 ν d ( neu t r on / f i ss i on s ) E n (MeV) Masters,1969Krick,1970Maksyutenko,1959Clifford,1972Herrmann,1966Notea,1969Benedict,1970Bucko,1966Brown,1971Piksaikin,2002
FIG. 32. Delayed neutron yield of uranium isotopes with A =233 to 238. The data are taken from Bobkov et al. [270],Loaiza et al. [216], Brady et al. [132], Gudkov et al. [214],and the evaluation by Tuttle [249, 263], while the IPPE dataare taken from Piksaikin et al. [227, 228, 230, 256, 257] andRoshchenko et al. [229]. . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
Pu-239 ν d ( neu t r on / f i ss i on s ) This WorkJENDL-4.0ENDF/B-VII.1JEFF-3.2Piksaikin,2006,2013Masters,1969Keepin,1957
Pu-239 ν d ( neu t r on / f i ss i on s ) Conant,1970Besant,1977Notea,1969Rose,1957Krick,1970Brunson,1955Cox,1974
Pu-240 ν d ( neu t r on / f i ss i on s ) This WorkJENDL-4.0ENDF/B-VII.1,JEFF-3.2Benedetti,1982Cesana,1980Keeipn,1957,1969
Pu-241 ν d ( neu t r on / f i ss i on s ) This WorkJENDL-4.0ENDF/B-VII.1JEFF-3.2Cox,1961Meadows,1976Cesana,1980Benedetti,1982Keepin,1969
Pu-242 ν d ( neu t r on / f i ss i on s ) E n (MeV) This WorkJENDL-4.0,ENDF/B-VII.1JEFF-3.2Krick,1972Bobkov,1989
FIG. 33. Delayed neutron yield of plutonium isotopes with A = 239 to 242. The data are taken from Bobkov et al. [270],Benedetti et al. [211], Cesana et al. [271, 272], and the eval-uation by Tuttle [249], while the IPPE data are taken fromPiksaikin et al. [230]. Figure 34 shows the delayed neutron activities forthermal neutron fission of U, Pu and
U.The activities are plotted as a function of time af-ter fission burst, t , and the figures compare the re-sults obtained with the current model with Keepin’ssix group constants [13] and the summation cal-culations using the fission product yields from theJENDL/FPY-2011 library and the radioactive decay datafrom the JENDL/FPD-2011 library (JENDL/FPY,FPD- 2011) [26]. For U, the present calculations andJENDL/FPY,FPD-2011 reproduce Keepin’s data rea-sonably. However, JENDL/FPY,FPD-2011 overesti-mates the delayed neutron activity at times t <
Pu and
U, the delayed neutron activities ofJENDL/FPY,FPD-2011 overestimate those of Keepin’ssix group evaluation [13] significantly, while the presentcalculations are rather close to Keepin’s results withinerrors.Figure 35 shows the delayed neutron activities for thefast neutron fission of U, U, U, Pu and
Pu.Similar to the results observed for thermal neutron fis-sion, the delayed neutron activity obtained with the newmodel calculations is close to Keepin’s six group evalu-ations within errors. JENDL/FPY,FPD-2011 overesti-mates Keepin’s data significantly except for U. U-235 DN a c t. x t i m e ( s / f i ss i on ) KeepinJENDL/FPY,FPD-2011This Work0.00000.00020.00040.00060.00080.00100.00120.00140.00160.0018
Pu-239 DN a c t. x t i m e ( s / f i ss i on ) KeepinJENDL/FPY,FPD-2011This Work0.00000.00020.00040.00060.00080.00100.00120.00140.00160.001810 -3 -2 -1 U-233 DN a c t. x t i m e ( s / f i ss i on ) Time after fission burst (s) KeepinJENDL/FPY,FPD-2011This Work
FIG. 34. Delayed neutron activities multiplied by time t afterneutron radiation for thermal neutron fission of U (top),
Pu (middle), and
U (bottom). Instant neutron radi-ation is assumed. The present calculation indicated by thedashed lines are compared with the summation calculation ofJENDL/FPY-2011 and FPD-2011 (JENDL/FPY,FPD-2011)[26] (solid line) and the results of Keepin’s six group [13] (er-rors are shown by the shade).
To conclude, the incident neutron energy dependenceof the delayed neutron yields of uranium and plutoniumisotopes was re-estimated with the model of Ref. [265] us-ing the new evaluated CRP data introduced in Sect. III.The present model reproduces the experimental total de-layed neutron yields reasonably well. Moreover, the de-layed neutron activities at thermal and fast neutron fis-sions evaluated by Keepin’s six group model are also wellreproduced.49evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al.
U-233 DN a c t. x t i m e ( s / f i ss i on ) KeepinJENDL/FPY,FPD-2011This Work0.00000.00050.00100.00150.00200.00250.00300.00350.00400.0045
U-235 DN a c t. x t i m e ( s / f i ss i on ) KeepinJENDL/FPY,FPD-2011This Work0.00000.00100.00200.00300.00400.00500.00600.00700.00800.00900.01000.0110
U-238 DN a c t. x t i m e ( s / f i ss i on ) KeepinJENDL/FPY,FPD-2011This Work0.00000.00020.00040.00060.00080.00100.00120.00140.001610 -3 -2 -1 Pu-239 DN a c t. x t i m e ( s / f i ss i on ) Time after fission burst (s) KeepinJENDL/FPY,FPD-2011This Work
FIG. 35. Same as Fig. 34, but for fast neutron fission of U, U, U, and
Pu.
However, new evaluations of fission yield data whichare able to reproduce both decay heat and delayed-neutron emission data simultaneously, using the summa-tion method, are urgently needed. New measurements oftotal delayed neutron yields at different incident neutronenergies are also important for the evaluation of both fis-sion yields as well as delayed neutron yields.
VI. SUMMATION CALCULATIONS
Summation and time-dependent calculations of totaldelayed neutron yields, delayed neutron spectra and de-layed neutron activities using the CRP evaluated micro-scopic ( T / , P n ) data are compared with recommendeddata and evaluated libraries in this section. The aim isto assess the new CRP data against a broad range ofavailable macroscopic data. A. A numerical ( T / , P n ) data file for practicalapplications A numerical file of definitive T / and P n values hasbeen created for use in summation and other calcula-tions for applications spanning fission reactor technolo-gies, anti-neutrino spectra and nuclear astrophysics. Thefile is based exclusively on the evaluated data producedby the CRP as described in Sect. III [43]. These data arepurely experimental without any input from systematicsor theory. It is left to the user to decide how to treatdiscrepant values (when compared with theory or sys-tematics) or missing values due to lack of experimentaldata.Furthermore, the “non-numerical” features of the( T / , P n ) tables, such as limits or approximate values,have been replaced with purely numerical values, andasymmetric limits have been symmetrized. A list of allthe modifications implemented in the numerical file withrespect to the tables available online is given below: • upper limits were symmetrized, i.e. if P n < . P n = 0 . ± . • lower limits are ’symmetrized’ as follows: P n > x becomes P n = y ± z so that x = y − z and 100 = y + z . When the latter cannot be enforced, then thelower limit is doubled with an uncertainty of 50%,i.e. y = 2 x and z = x , with y + z = 3 x ≤ • asymmetric uncertainties were symmetrized follow-ing the prescription: x ( ab ) → y ± z ; y = x + a − b , z = a + b • approximate values were assigned 50 % uncertainty,i.e. P n ≈ . P n = 0 . ± . • when multiple activities are measured but cannotbe distinguished, i.e. when a P n is given for boththe ground state and isomeric states, then the latteris split equally among the states while the uncer-tainty for each state remains the same as the orig-inal recommended one. As an example, one takesfor Ga a recommended value for both, the groundstate and the isomeric state , of P n = 0.90(7)% .In the numerical file, the value P n = 0.45(7)% wasadopted for the ground state and isomeric state, re-spectively. If the original uncertainty is larger thanthe split P n value, one can adopt a 100% uncer-tainty for the split value. For example, in the caseof Rh, where P n < .
1% for both ground stateand isomeric state, the limit is symmetrized to give P n = 1 . ± .
05 % and the resulting P n is splitamong the two states with 100% uncertainty, i.e.as P n = 0 . ± .
525 % for the ground state andisomeric state, respectively.50evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al. • there are a few cases ( , Al, P) where the re-ported measured P n value can take unphysical val-ues within the reported uncertainty range. In suchcases the uncertainty was adjusted so that P n lieswithin the physical limits (0 ≤ P n ≤
100 %). • zero values for Q βxn and P xn have the followingmeaning: (i) there are no measurements available,(ii) the decay mode is forbidden. • nuclides that have only been identified in measure-ments and have no measured T / or P n value arenot included in the numerical file.The format of the file is as follows:Nuclide name, Z, A, liso (index indicating order of states,i.e. for ground state liso = 0, for 1st isomeric state liso= 1, etc.), Level Energy, ∆ Level Energy, % β − , ∆% β − , Q βn , ∆ Q β n , Q βn , ∆ Q β n , Q βn , ∆ Q β n , T / , ∆ T / , P n , ∆ P n , P n , ∆ P n , P n , ∆ P n .The numerical file has been used in the summation cal-culations described in the following sections with the aimof verifying and validating the new evaluated P n tablesproduced by the CRP. It is available for downloading atthe IAEA Beta-delayed neutron database [43]. A moredetailed description of the contents of the IAEA Beta-delayed neutron database is given in Section X. B. Total delayed neutron yields
1. Basic summation calculations
In this section, summation calculations of the totaldelayed neutron yield ν d performed with the CRP data( T / , P n ) are compared with other decay data librariesand with recommended values. a. Comparison with evaluated libraries. The firststep in verifying and testing the new evaluated CRP( T / , P n ) values using the numerical file was to performa basic inter-comparison of summation calculations of thedelayed neutron yields among the CRP participants. To-tal delayed neutron yields (DN) were calculated for ther-mal and fast neutron-induced fission of major and mi-nor actinides by four independent groups, namely CEA-Cadarache (Foligno), CIEMAT (Cano), JAEA (Minato)and SUBATECH-Nantes (Fallot).The calculations are based on the summation methodwhereby the total delayed neutron yield ν d is defined as ν d = (cid:88) i N ni · CF Y i (24)where N ni is the average delayed neutron multiplic-ity emitted by the precursor i and is given by N n =1 · P n + 2 · P n + 3 · P n ... , P xn are the delayed neutronemission probabilities P xn and CF Y i are the cumulativefission yields for precursor i. The above equation holds for equilibrium irradiation where the production and de-cay rates of the precursor nuclides are proportional totheir cumulative fission yields.Assuming the N n and CF Y quantities in the aboveexpression are independent, the uncertainty of the totalDN yield is given by σ ν d = (cid:88) i N ni · σ CF Y i + (cid:88) i σ N n i · CF Y i (25)where σ N n i and σ CF Y i are the uncertainties of the de-layed neutron multiplicities N ni and cumulative fissionyields CF Y i of the individual precursors.In the following calculations, the cumulative fissionyields CF Y i are taken from the JEFF-3.1.1 fission yield li-brary [28] which has been widely tested in a broad rangeof applications, including in summation calculations ofDN yields, and has proved to perform well. The β − decay and β -delayed neutron data, ( T / , P n ), are taken fromthe new CRP tables. Nuclides for which there are no P n values in the new CRP tables are not considered as β -delayed neutron emitters, i.e. P n = 0. The remain-ing decay data ( γ decays-IT), when used in the basicsummation calculations or time-dependent calculations,are taken from ENDF/B-VIII.0 [25]. This combinationof input data is hereafter referred to as CRP+ENDF/B-VIII.0. The calculations are compared with total DNyields obtained by combining CF Y i from JEFF-3.1.1 anddecay data from the ENDF/B-VIII.0 decay data sub-library. This comparison enables us to observe the di-rect impact of the new CRP data ( T / , P n ) on the to-tal DN yields as all the other data inputs are the same.It is also interesting to explore the differences betweenthe new improved CRP+ENDF/B-VIII.0 decay data sub-library and the other available evaluated decay-data sub-libraries. Therefore, additional calculations were per-formed by combining the CF Y i from JEFF-3.1.1 [28] withthe decay data from JEFF-3.1.1 [28] and JENDL/DDF-2015 [27] sub-libraries. Note that the release of JEFF-3.3library occurred after most of the work carried out by theCRP was completed. Since JEFF-3.3 and JEFF-3.1.1 donot differ with respect to the DN data, it was decidedthat for the purposes of the CRP work it was sufficient topresent the results that had already been obtained withJEFF-3.1.1 as they would in practice be identical withthose obtained with JEFF-3.3.The results of the summation calculations for the majoractinides U, U, , Pu are given in Table VI. Per-fect agreement is observed among the four different sum-mation calculations which confirms that the calculationsperformed by the different groups within this project areequivalent and hence reliable. We do not need to reportthe results of all four groups hereafter, but just the re-sults of the CRP. The values in Table VI are considered asreference values for the given combination of decay dataand fission product yields library.The results displayed in Table VI show that overallthe CRP P n data lead to larger values of the total DN51evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al. T A B L E V I . T o t a l d e l a y e dn e u t r o n y i e l d s ( ν d ) f o r t h e r m a l a nd f a s t n e u t r o n - i ndu c e dfi ss i o n o f m a j o r a c t i n i d e s o b t a i n e d f r o m t h e s u mm a t i o n m e t h o du s i n g t h r ee d i ff e r e n t d e c a y d a t a li b r a r i e s ( C R P + E N D F / B - V III . , E N D F / B - V III . , J E FF - . . , J E N D L / DD F - ) i n c o m b i n a t i o n w i t h t h e c u m u l a t i v e fi ss i o n y i e l d s C F Y f r o m J E FF - . . . F o u r g r o up s p a r t i c i p a t e d i n t h e i n t e r - c o m p a r i s o n , n a m e l y C E A ( F r a n c e ) , C I E M A T ( Sp a i n ) , J A E A ( J a p a n ) , a nd NAN T E S ( F r a n c e ) . T h e nu m b e r s i nb r a c k e t s a r e t h e r e l a t i v e un c e r t a i n t i e s n e g l e c t i n g c o rr e l a t i o n s . C R P + E N D F / B - V III . d e c a y d a t a t h e r m a l f a s t ν d C E A C I E M A T J A E ANAN T E S C E A C I E M A T J A E ANAN T E S U . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) U . ( % ) . ( % ) . ( % ) . ( % ) P u . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) P u . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) E N D F / B - V III . d e c a y d a t a t h e r m a l f a s t ν d C E A C I E M A T J A E ANAN T E S C E A C I E M A T J A E ANAN T E S U . ( % ) . ( . % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) U . ( % ) . ( % ) . ( % ) . ( % ) P u . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) P u . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) J E FF - . . d e c a y d a t a t h e r m a l f a s t ν d C E A C I E M A T J A E ANAN T E S C E A C I E M A T J A E ANAN T E S U . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) U . ( % ) . ( % ) . ( % ) . ( % ) P u . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) P u . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) J E N D L / DD F - d e c a y d a t a t h e r m a l f a s t ν d C E A C I E M A T J A E ANAN T E S C E A C I E M A T J A E ANAN T E S U . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) U . ( % ) . ( % ) . ( % ) . ( % ) P u . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) P u . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . ( % ) . . . NUCLEAR DATA SHEETS P. Dimitriou et al. yields ( ν d ) compared to the other evaluated decay datalibraries ENDF/B-VIII.0, JEFF-3.1.1 and JENDL/DDF-2015. The observed differences are larger with respectto JEFF-3.1.1, which generally gives the lowest valuesof total DN yields among all three evaluated libraries.In the case of fast fission of U and thermal fission of
Pu, the CRP+ENDF/B-VIII.0 total DN yields are inagreement with the ENDF/B-VIII.0 and JENDL/DDF-2015 results.The 20 most important contributors to the total DNyields ( ν d ) displayed in Table VI are listed in Table VII.The first column includes the percentage contributionof the precursors resulting from the CRP ( T / , P n )data, while the neighboring columns include the con-tributions of the same precursors obtained when us-ing the ENDF/B-VIII.0, JEFF-3.1.1 and JENDL/DDF-2015 decay data, respectively. Both ENDF/B-VIII.0and JENDL/DDF-2015 have adopted P n values fromENSDF [23], however, depending on the date they wereretrieved from the ENSDF database, the values may dif-fer among each other and with respect to the currentENSDF data value. JEFF-3.1.1 uses P n values from anevaluation by Nichols [30] as well as from ENSDF.From Table VII we see that overall, the differences be-tween the contributions of the top 20 precursors amongthe various libraries are less than 10%. Some notablecases are discussed below: I is the main contributor to ν d for nearly all themajor actinides and incident neutron energies. The Icontribution is enhanced (on average by a few %) whenusing the CRP data and is mainly responsible for thesmall increase in the total DN yields observed in Table VI.The increased relative contribution of
I is related to asmall increase in the CRP P n value for this precursor,which is now P n = 7 . . P n = 6 . As is among the top twelve contribu-tors in the CRP list with P n = 62 . P n = 59 . P n = 22(3)% adopted in JEFF-3.1.1 [30]. Br is among the top 20 contributors in the CRP listwith P n = 29 . P n = 20(2)% taken from [30] and JENDL/DDF-2015 P n = 20(3) taken from ENSDF. In ENDF/B-VIII.0,however, this precursor does not have a delayed-neutrondecay branch, therefore it does not contribute to the de-layed neutron activity. Te appears in the top 20 list of the CRP calculationsalthough it has a relatively small β -delayed neutron frac-tion of P n = 1 . P n = 1 . Br to the CRP list is lower bymore than 13% in comparison to JEFF-3.1.1. This differ-ence is observed across several of the major actinides, andis related to the small difference in P n values, with P n =13 . P n = 14 . P n = 13 . P n values may have a non-negligible impact on theDN group spectra which are estimated from summationsover the energy spectra of individual precursors weightedby their relative contributions to the total DN yield, inaddition to the differences observed in the total delayedneutron yields.The uncertainties associated with the new total DNyields in Table VI are fairly small compared to thelarge uncertainties affecting the cumulative fission yieldsCFYs. However, this is expected considering that theestimation of the uncertainties ignores the effect of cor-relations which are particularly strong between the CFYuncertainties. A more rigorous treatment of the propa-gation of uncertainties including correlations would yielddifferent results. b. Comparison with recommended values. The totalDN yields presented in Table VI are compared with rec-ommended DN yields from [246] and the recommendedDN yield data from JEFF-3.1.1, ENDF/B-VIII.0 andJENDL-4.0 [258] libraries in Figs. 36-38. It should benoted that the total DN yields from JEFF-3.1.1 are iden-tical to the JEFF-3.3 data therefore the results in Fig. 36are valid for both libraries. As shown in the figures, thetotal DN yields obtained with the CRP ( T / , P n ) data forthermal fission of U and
Pu are in good agreementwith the recommended data [246] and the data from theother libraries except for the thermal value of
Pu fromJENDL-4.0. The results for the fast fission of
U aresubstantially closer to the recommended data comparedwith the previous summation calculations of [187]. Thedifferences between the calculated and recommended val-ues of the total DN yields for the fast neutron-inducedfission of
Pu and
U and for both fast and ther-mal fission of
Pu are more than 10%. These differ-ences highlight the need for better treatment of uncer-tainties and further improvement of the microscopic datafor these nuclides, mainly the fission yield data. Anotherimportant feature of the CRP results presented in Ta-ble VI is the clear evidence of the energy dependence ofthe total DN yields for fission of
U and
Pu. This isin agreement with the latest experimental data presentedin this paper (see Section V C) and supports the need forfurther investigation of this dependency.53evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 36. Comparison of the total DN yields obtained fromthe summation method using the CRP ( T / , P n ) data andthe JEFF-3.1.1 decay-data sub-library, respectively, with therecommended DN yields [246]. The total DN yields for thefission of various nuclides (listed on the abscissa axis) are plot-ted with symbols. The right ordinate shows the percentagedifference between the total DN yield data calculated usingthe CRP data and the corresponding data from JEFF-3.1.1(bar chart).FIG. 37. Same as in Fig. 36 but for the ENDF/B-VIII.0 decaysub-library.
2. Time-dependent calculations
Apart from summation calculations that use cumula-tive fission yields to account for the abundances of thefission products in equilibrium, time-dependent calcula-tions that start from independent fission yields and followthe evolution of the system into the decay phase, can alsoshed light on the impact of the new CRP ( T / , P n ) dataon integral quantities. In this section, we describe twodifferent time-dependent calculations of the integral DNactivity and total DN yields that were performed with FIG. 38. Same as in Fig. 36 but for the JENDL-4.0 decaysub-library (bar chart). the new CRP data. a. Time-dependent calculations during the irradiationand decay phase.
The integral DN activity experimentis simulated by summing up the microscopic contributionof each of the precursors produced during the fission pro-cess. The Bateman solver [262] is a computer programthat uses the decay data to reconstruct the family treeof the precursors and then solves the Bateman equationsto obtain the precursors’ concentration during both theirradiation and the decay phase. The concentrations-in-time are then multiplied by the effective delayed-neutronemission probability of the precursor (Eq. 26). n d ( t ) = N (cid:88) i =1 C i ( t ) P n eff i , (26)where P n eff i = (cid:80) x =1 x P xn is the effective delayed-neutron emission probability of the precursor i , whichtakes into account multiple decay branches leading to theneutron emission. The following decay-processes are con-sidered in the code [262]: IT , β − , β − n , β − n , β − n and β − n .The Bateman solver has been validated through compar-isons with the DARWIN code [273].Figure 39 shows the DN activity for thermal neutron-induced fission of U computed by combining theCRP+ENDF/B-VIII.0 and ENDF/B-VIII.0 decay datawith JEFF-3.1.1 fission yields. The figure shows the twoDN activities as w ell as their ratio, as a function of timeafter the irradiation.The ratio does not start from 1 because the ν d isdifferent (1.60 neutrons/100 fissions for ENDF/B-VIII.0and 1.66 neutrons/100 fissions for CRP+ENDF/B-VIII.0for U). Table VIII displays the 20 most importantprecursors according to the CRP calculations (see alsoTable VII), together with their partial yield ν d,i , thedifference with respect to the partial yields calculated54evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al. T A B L E V II . T h e t w e n t y m o s t i m p o r t a n t c o n t r i bu t o r s t o ν d f o r t h e r m a l a nd f a s t n e u t r o n - i ndu c e dfi ss i o n o f t h e m a j o r a c t i n i d e s U , U , P u a nd P uu s i n g t h e C R P + E N D F / B - V III . d e c a y d a t a ( C R P ) . I n c o l u m n s ’ E N D F / B ’,’ J E FF ’ a nd ’ J E N D L ’, w e g i v e t h e c o n t r i bu t i o n s o f t h e s e p r e c u r s o r s o b t a i n e d w h e nu s i n g E N D F / B - V III . , J E FF - . . nd J E N D L / DD F - d e c a y - d a t a li b r a r i e s , r e s p e c t i v e l y . A ll t h e c o n t r i bu t i o n s a r e g i v e n i n % . U t h e r m a l U f a s t U f a s t N u c li d e C R PE N D F / B J E FF J E N D L N u c li d e C R PE N D F / B J E FF J E N D L N u c li d e C R PE N D F / B J E FF J E N D L I . . . . R b . . . . I . . . . B r . . . . I . . . . R b . . . . R b . . . . B r . . . . B r . . . . B r . . . . B r . . . . B r . . . . B r . . . . B r . . . . A s . . . . A s . . . . m Y . . . . I . . . . I . . . . A s . . . . Sb . . . . m Y . . . . R b . . . . B r . . . . I . . . . I . . . . I . . . . R b . . . . R b . . . . R b . . . . R b . . . . B r . . . . B r . . . . B r . . . . Y . . . . C s . . . . B r . . . . B r . . . . R b . . . . Y . . . . I . . . . Y . . . . Sb . . . . C s . . . . m Y . . . . T e . . . . R b . . . . R b . . . . C s . . . . A s . . . . Sb . . . . A s . . . . Sb . . . . I . . . . R b . . . . T e . . . . I . . . . T e . . . . R b . . . . R b . . . . P u t h e r m a l P u f a s t P u t h e r m a l P u f a s t N u c li d e C R PE N D F / B J E FF J E N D L N u c li d e C R PE N D F / B J E FF J E N D L N u c li d e C R PE N D F / B J E FF J E N D L N u c li d e C R PE N D F / B J E FF J E N D L I . . . . I . . . . I . . . . I . . . . R b . . . . R b . . . . I . . . . R b . . . . m Y . . . . m Y . . . . R b . . . . I . . . . B r . . . . B r . . . . I . . . . B r . . . . I . . . . B r . . . . m Y . . . . m Y . . . . B r . . . . A s . . . . B r . . . . R b . . . . R b . . . . B r . . . . Sb . . . . B r . . . . Y . . . . Y . . . . Y . . . . I . . . . B r . . . . R b . . . . B r . . . . A s . . . . R b . . . . R b . . . . R b . . . . Y . . . . I . . . . B r . . . . B r . . . . B r . . . . A s . . . . I . . . . A s . . . . N b . . . . B r . . . . B r . . . . T e . . . . R b . . . . Sb . . . . N b . . . . R b . . . . Sb . . . . C s . . . . I . . . . C s . . . . B r . . . . T e . . . . R b . . . . N b . . . . C s . . . . N b . . . . C s . . . . B r . . . . T e . . . . B r . . . . A s . . . . T e . . . . R b . . . . R b . . . . T e . . . . B r . . . . N b . . . . T e . . . . Sb . . . . C s . . . . B r . . . . . . . NUCLEAR DATA SHEETS P. Dimitriou et al. −3 −2 −1 Time after irradiati n [s]0.00000.00250.00500.00750.01000.01250.0150 n d ( t ) [ D N / s ] ENDF/B-VIII.0 CRP10 −3 −2 −1 Time after irradiation [s]0.970.980.991.001.011.021.031.04 n d , C R P / n d , E N D F / B − V III . [ - ] FIG. 39. Comparison between the CRP+ENDF/B-VIII.0 andENDF/B-VIII.0 decay data. The two plots represent the twoDN activities and their ratio, respectively, following the ther-mal fission of U. with ENDF/B-VIII.0, and the change in the correspond-ing precursor P n emission probability when going fromENDF/B-VIII.0 to CRP+ENDF/BVIII.0.The discrepancies observed in the partial ν d,i of thefirst 20 precursors are responsible for a difference in thetotal ν d of +7.3 × − . The fact that, when consid-ering all the precursors, such a difference decreases to+6.4 × − , means that there is a compensation due tothe underestimation of less important precursors in theCRP P n tables with respect to the ENDF/B-VIII.0 de-cay library. From a comparison of the individual iso-topes, it appears that the largest ∆ ν d,i belongs to Iand Br. The latter precursor in particular, has P n =0 in ENDF/B-VIII.0, whereas in the previous versionENDF/B-VII.1 [24] it had a non-zero P n value. Thisis quite a marked difference between the libraries sincein the recommended CRP tables this β -delayed neutronprecursor alone, accounts for almost 3% of the ν d .As far as the results for the DN activity shown inFig. 39 are concerned, the two absolute activities seemto agree perfectly, however their ratio shows a discrep- TABLE VIII. Detailed comparison of the microscopic data ofthe 20 most important precursors for thermal neutron-inducedfission of
U: atomic number ( Z ), mass ( A ), isomeric num-ber (index) ( I ), the partial delayed neutron yield computedby using CRP+ENDF/B-VIII.0 decay data ( ν d,i ), the differ-ence in the partial yield when using CRP+ENDF/B-VIII.0rather than ENDF/B-VIII.0 (∆ ν d,i ) and the change in mi-croscopic P n from ENDF/B-VIII.0 to CRP+ENDF/B-VIII.0( P n (VIII.0) → P n (CRP)). Z A I ν d,i ∆ ν d,i P n (VIII.0) → P n (CRP)53 137 0 2.72 × − × − → × − –1.365 × − → × − –1.64 × − → × − × − → × − × − → × − × − → × − –3.82 × − → × − × − → × − –1.555 × − → × − × − → × − × − → × − –1.50 × − → × − × − → × − × − → × − –3.57 × − → × − × − → × − –9.55 × − → × − –4.45 × − → × − × − → × − –3.85 × − → × − Sum(all) 0.0167 +6.4 × − ancy that varies from +4% after about 30 s to -3% after400 s. The relative uncertainty in these calculations hasbeen estimated to increase with time, due to the modelthat is used. At the beginning of the decay (just after aninfinite irradiation), the activity corresponds to the ν d , sothe uncertainty associated with the two points is about5% per point. This means that the ratio has an uncer-tainty of about 7% (not taking into account the correla-tions induced from using the same fission yields). This isthe time after irradiation at which the deviation betweenthe 2 curves is at its maximum (4%). Therefore, whenthe deviation between the two curves is at its maximum(4%), the uncertainty is at its minimum (7%), and wemay conclude that the two DN activity curves agree.The variations observed in the ratio of the DN activitiesare due to the differences in the P n values of the I and Br precursors in the two libraries. As can be seen inTable VIII, the I P n value from the CRP is increasedwhile the corresponding Br P n value is decreased. Thisexplains the bump at 30 s - where the importance of Iis maximum - as well as the -3% plateau that extends tillthe end of the decay when only Br is left.Figure 40 shows the relative contribution of the mostimportant precursors as a function of time. It is clear that
I dominates after about 30 s from the end of the irra-56evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al. -2 Time [s] R e l a t i v e c on t r i bu t i on [ % ] I137Br89Rb94Br90Br88 As85Y98mRb95I139Br87 Rb93Br91Sb135Y99Te136
FIG. 40. Relative contribution of the most important pre-cursors in time, following the thermal fission of U t . It isclear that I dominates after about 100 s from the end ofthe irradiation, while after 300 s the activity is only due to Br diation, while after 300 s the activity is only due to Br.The latter finding for Br is quite interesting, as thisprecursor did not appear among the most important con-tributors in the basic summation calculations discussed inthe previous section. This confirms that time-dependentcalculations allow us to gain deeper insight in the roleof each DN precursor in the β -delayed neutron processfollowing fission.Overall, as seen in the previous section, the CRP P n data differ from those adopted in the ENDF/B-VIII.0 de-cay data library for several precursor nuclides. In time-dependent calculations, these differences lead to differentprecursor family trees, both in shape and intensity , whereintensity is the amount of precursors created by the fa-thers’ decay. The impact of the new CRP ( T / , P n ) datais evident in the ν d and DN activity ratio. In particular,the shape of the curve in the decay phase is stronglyaffected by the microscopic data of the long-lived precur-sors, namely I and Br. b. Time-evolution calculations of major and minoractinides at thermal, fast and spallation energies.
TheCRP data have also been used in time-evolution calcula-tions of the composition of pure spheres filled with majorand minor actinides. The calculations have been per-formed at three incident neutron energies (thermal, fastand spallation) for which fission yield data are availablein the evaluated libraries. To begin with, the JEFF-3.1.1independent fission yields were combined with the JEFF-3.1 decay data to compute the activities at various timesteps using the MURE code [274]. The total DN yieldsper fission ν d were then calculated by means of the sum-mation method using the P n values obtained from theCRP, ENDF/B-VIII.0 and the JEFF-3.1.1 libraries. Theresults are compared with the recommended values of ν d found in the JEFF-3.1 evaluated library (Table IX).A first observation from Table IX is that the informa- tion on delayed neutron yields available in the evaluateddatabase JEFF-3.1 is sparce. For example, there is novalue available in the fast range for U, while for sev-eral actinides ν d values are provided at rather different’fast’ energies, i.e. 200 keV in one case and 4 MeV inanother case.Nevertheless, from the comparison of the results ob-tained at the available incident energies we observe simi-lar trends: the ν d values obtained with the CRP P n data(third column in Table IX) are systematically larger thanthose obtained with the ENDF/B-VIII.0 (fourth column)and JEFF-3.1.1 P n data (fifth column). The results ob-tained with JEFF-3.1.1 decay data are the lowest of thethree and deviate from the recommended values the most.This is in agreement with the findings of Sect. VI B 1.For major actinides in the thermal range (fast in thecase of U), the ν d s obtained from the summation cal-culations are quite close to the recommended values ofJEFF-3.1.1 (second column). ENDF/B-VIII.0 is in bet-ter agreement with recommended JEFF-3.1.1 values inthe case of U and
Pu, while for
U and
Pu theCRP data are closer to the recommended values. How-ever, once the conditions regarding fuel or impinging neu-tron energy differ from those of a pressurized water re-actor (PWR), the discrepancies among the summationcalculations and recommended values increase. Overallthe three summation calculations (using different inputdata) are in better agreement among themselves thanwith the recommended ν d values of JEFF-3.1.1. The in-troduction of the new CRP P n values does not lead toan improvement with respect to the recommended val-ues, but rather enhances the discrepancies, with the soleexception of U and
Pu as already mentioned. Thisis due to the enhanced P n values of the most importantcontributors which was also observed in the previous sec-tions VI B 1 and VI B 2 a.The results show that additional work is needed to im-prove the other microscopic data used in the summationcalculations besides the β -delayed neutron emission data,i.e. the fission yield data. It is of high importance toimprove the evaluated fission yield data for a range ofincident neutron energies needed in various applications.Furthermore, considering the inconsistencies observed insome of the recommended data in JEFF-3.1.1 (identicalvalues for thermal and fast fission), and the availabilityof integral data at incident neutron energies that are notdirectly comparable with those of the fission yields, it isclear that new integral measurements of ν d is merited. C. Time-dependent delayed-neutron integralspectra
In this section we use the new CRP ( T / , P n ) datain calculations of time-dependent DN integral spectrafor thermal neutron-induced fission of U and comparethem with measured, as well as recommended spectra inthe existing evaluated libraries.57evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al.
TABLE IX. Delayed neutron yields ν d obtained from simulations of individual fuels with thermal (”t”), fast (”f”) and spallation(”s”) independent fission yields from JEFF-3.1.1 coupled to JEFF-3.1 half-lives and P n values from the CRP (3rd column),ENDF/B-VIII.0 (4th column) and JEFF-3.1.1 (5th column). The ν d recommended in JEFF-3.1 are displayed in the 2nd column.In cases where the energies of the impinging neutrons differ substantially from the average neutron energies associated with thefission yields, the energies at which the ν d were extracted from JEFF-3.1 are given in parentheses. Nucleus ν d in JEFF-3.1 ν d from CRP P n ’s ν d from ENDF/B-VIII.0 P n ’s ν d from JEFF-3.1.1 P n ’s U t 6.73E-3 8.07E-3 7.82E-3 7.24E-3
U f x 1.16E-2 1.12E-2 1.04E-2
U s 4.39E-3 (14 MeV) 6.40E-3 6.19E-3 5.59E-3
U t 1.62E-2 1.66E-2 1.60E-2 1.47E-2
U f 1.63E-2 (200 keV) 1.87E-2 1.80E-2 1.70E-2
U s 8.9E-3 (12 MeV) 1.04E-2 9.8E-3 9.3E-3
U f 4.78E-2 (3.5 MeV) 4.6E-2 4.5E-2 4.1E-2
U s 1.88E-2 (20 MeV) 2.75E-2 2.58E-2 2.37E-2
Th f 5.27E-2 (4 MeV) 6.35E-2 6.11E-2 5.39E-2
Th s 3.0E-2 (7-20 MeV) 3.61E-2 3.35E-2 3.05E-2
Np t 1.2E-2 1.27E-2 1.23E-2 1.13E-2
Np f 1.2E-2 (2 MeV) 1.31E-2 1.26E-2 1.17E-2
Pu t 4.71E-3 3.51E-3 3.41E-3 3.19E-3
Pu f 4.71E-3 (7 MeV) 5.3E-3 5.1E-3 4.8E-3
Pu t 6.5E-3 6.8E-3 6.6E-3 6.0E-3
Pu f 6.51E-3 (200 keV) 7.51E-3 7.23E-3 6.75E-3
Pu f 9.0E-3 (9 MeV) 1.03E-2 9.9E-3 9.2E-3
Pu t 1.60E-2 1.39E-2 1.37E-2 1.23E-2
Pu f 1.60E-2 (5 MeV) 1.46E-2 1.41E-2 1.29E-2
Pu f 1.83E-2 (6 MeV) 1.90E-2 1.85E-2 1.68E-2
Am t 4.27E-3 4.22E-3 4.08E-3 3.79E-3
Am f 4.27E-3 (4 MeV) 4.58E-3 4.42E-3 4.15E-3
In Figs. 41-44, the spectra measured for thermalneutron-induced fission of
U at different time inter-vals by [243] as described in Section V B 2 are comparedwith the corresponding spectra calculated on the basisof the microscopic delayed neutron data, namely, the de-layed neutron spectra from individual precursors [41], theemission probability of delayed neutrons P n and the half-life of delayed neutron precursors T / taken from theCRP tables ( T / , P n ). Three sets of delayed neutronspectra were used in the calculations. The first one is thedelayed neutron spectra from the ENDF/B-VII.1 [24] de-cay data file which has been developed by Brady andEngland [132]. These data comprise thirty four exper-imental spectra combined and adjusted on the basis ofthe raw spectra data measured in Mainz [19], Studsvik[15, 16] and INEL [17, 18] and additionally, the spectrafor 235 nuclides calculated with the help of the evapo-ration model. The second set of energy spectra repre-sents the data from the ENDF/B-VII.1 file in which thespectra for − Br, − Rb,
Te, − I, − Csprecursors were replaced by the corresponding data ofGreenwood et al. [17, 18]. The third set is the 8-groupspectra from the JEFF-3.1.1 file [28]. The cumulative fis-sion yield data used in all these calculations were takenfrom the JEFF-3.1.1 FY file [28].The energy spectra in definite time-windows were cal-culated with the help of the time-dependent formula writ- ten for N delayed neutron precursors [243] χ ( E n , t ) dE n = A · N (cid:88) i =1 (cid:18) P ni · CY i λ i (cid:19) (cid:0) − e − λ i · t irr (cid:1) × (cid:0) e − λ i · t d (cid:1) (cid:0) − e − λ i · ∆ t c (cid:1) T i χ i ( E n ) dE n , (27) T i = (cid:34) n − e − λ i · T − e − λ i · T · − e − nλ i T (1 − e − λ i · T ) (cid:35) , where T i term describes the dependence of delayed neu-tron activity on the number of cycles; A the saturationactivity; P ni the emission probability of the i-th precur-sor; CY i the cumulative yield of the i -th precursor takenfrom JEFF-3.1.1 file [28]; χ i ( E n ) the delayed neutron en-ergy spectrum associated with the i-th precursor; λ i thedecay constant of the i -th precursor; t irr the irradiationtime, s; t d the delay time (cooling), s; ∆ t c the neutroncounting time (time window); n the number of cycles; T the period of one cycle (irradiation-cooling-counting-delay).As can be seen from Figs. 41 and 42 both the gen-eral form and peak structure of the summation spectrain time intervals 2-12 s, 12-22 s, 22-32 s, 32-152 s and inthe whole energy range are in excellent agreement with58evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 41. Comparison of the integral delayed spectra obtained from thermal neutron-induced fission of
U in the time intervals0.12-2 s, 2-12 s, 12-22 s, 22-32 s [243] with corresponding spectra calculated by means of the summation method using differentsets of microscopic delayed neutron data (irradiation time of experiments - 120 s). the corresponding integral spectra measured with the ir-radiation time 120 s. In the first time interval 0.12-2 sboth summation data overestimate the low-energy part ofthe energy spectrum as compared with the experimentaldata but nevertheless, they show the same peak struc-ture at 10, 50, 80, 120 and 170 keV. Upon inclusion inthe ENDF/B-VII.1 decay data file [24] of the Greenwood et al. spectra for precursors − Br, − Rb,
Te, − I, − Cs [17, 18], the agreement between theENDF/B-VII.1 based summation spectra and the exper-imental data severely deteriorates (see Figs. 41 and 43).The main difference between these spectra is that thelow-energy part of the spectrum (below 100 keV) is heav-ily overestimated when the Greenwood precursor spectraare included. The summation energy spectra calculatedon the basis of the 8-group data are very close to theENDF/B-VII.1 based data [24]. This observation can beconsidered as a clear indication that the procedure usedfor the generation of the 8-group spectra from microscopicdata is reliable and that the 8-group spectra reproduce the time evolution of the composite spectra. In the case ofthe short irradiation data (see Fig. 44), we observe goodagreement between experimental and calculated spectradata in the 4-44 s time interval except for some deviationsat the high energy peaks at 740, 850, 950, 1050, and 1140keV, which are overestimated in the summation spectra.The main difference between the summation spectra andexperimental short irradiation data in the other time in-tervals is the low intensity of the 317 and 352 keV peaksand the unresolved peaks at about 420 and 513 keV inthe summation spectra (see Fig. 43).Thus, the agreement between the summation and com-posite experimental spectra observed in the long irradi-ation data validates the approach taken by Brady andEngland [132] in developing the ENDF/B-VII.1 precur-sor spectra. Furthermore, this agreement justifies ourconfidence in the summation method using the currentmicroscopic CRP β -delayed neutron database. The dis-crepancies observed in the short irradiation data show thenecessity to continue efforts to improve the microscopic59evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 42. Thermal neutron-induced fission of
U. Left side: comparison of the integral delayed spectra in the time interval32-152 s [243] with corresponding spectra calculated by means of the summation method using different sets of microscopicdelayed neutron data. Right side: the integral delayed spectra in the time interval 0.12-2 s. The Greenwood et al. [17, 18]spectra are added to the ENDF/B-VII.1 data base [24] (irradiation time of experiments - 120 s). data on the short-lived precursor spectra on the basisof the up-to-date model developed by [32]. The IPPEintegral energy spectra obtained from thermal neutron-induced fission of
U in different time intervals [243]that were successfully used in the comparison studies inthis section, should be used further as a benchmark forboth testing individual precursor spectra and improvingthe short-lived group spectra.
D. Time-dependent delayed-neutron parameters
The CRP data are also used to calculate time-dependent parameters in the 8-group model. For thispurpose, the DN activity curve is obtained from summa-tion calculations over the microscopic β -delayed neutronCRP data ( T / , P n ). The 8-group parameters ( a i , λ i )are extracted from the activity curve and compared withrecommended 8-group parameters [14]. This is anotherway of assessing the impact of the CRP ( T / , P n ) dataon integral quantities. a. Time-dependent parameters from microscopic cal-culations The delayed neutron-activity is simulatedthrough microscopic summation calculations, as ex-plained in Subsection VI D. Fission Yields (FY) are takenfrom JEFF-3.1.1 and Radioactive Decay Data (RDD)from CRP+ENDF/B-VIII.0 and ENDF/B-VIII as de-scribed in Section VI B 1. Where needed, the excitationstate of the daughter nucleus after the decay (
RF S ) istaken from ENDF/B-VIII.0 [25].The DN activity obtained from the summation calcula-tions is then fitted by the CONRAD code [275], which isdeveloped at CEA (France) with the purpose of perform-ing high-quality uncertainty analysis. Instead of fittingthe delayed neutron activity directly, we have chosen to fit the difference between the two models: microscopicand macroscopic (Eq. 28). n d ( t ) n d (0) − (cid:88) i =1 a i (1 − e − λ i t irr ) e − λ i ( t − t irr ) = 0 , (28)where t irr is the irradiation time and n d (0) is the DNemission rate at the end of the irradiation phase, whichcorresponds to the average DN yield in case of an infiniteirradiation.The CONRAD code implements Baye’s theorem, whichallows adjusting the model parameters - in this case, thegroup abundances - according to the available experimen-tal information. In this work, however, the experimentaldata are replaced by the calculated DN emission rates.The parameters of the macroscopic model are thereforeadjusted to fit the microscopic model. This procedure,coupled with an analytical marginalization technique, al-lows one to propagate the uncertainty in hundreds of mi-croscopic data to just the eight abundances a i . At thesame time, CONRAD provides the correlations amongthe uncertainties of the fitted parameters (see Fig. 45),which compensate for the apparently higher uncertaintyin the single abundances.The results of the simulation of the experiment, i.e. ofthe DN activity curve, and the subsequent extraction ofthe group parameters are presented in Tab. X. The associ-ated uncertainties given in brackets reflect the uncertain-ties arising from the hundreds of parameters marginalizedin the CONRAD fit. Tables XI to XXI display the cor-relation matrices of the abundances obtained with theanalytical marginalization technique. The small correla-tions among the abundances derive from the fact thateach group is responsible for a part of the decay curve60evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 43. Comparison of the integral delayed spectra obtained for thermal neutron-induced fission of
U in the time intervals0.12-1 s, 1-2 s, 2-3 s and 3-4 s [243] with corresponding spectra calculated by means of the summation method using differentsets of microscopic delayed neutron data (irradiation time of experiments - 20 s). and is supposed to represent only those precursors hav-ing a similar half-life. A physical correlation among abun-dances could only arise from the family tree, for exam-ple, a short-lived precursor being created by the decay ofa long-lived precursor. This would create a small corre-lation between the two groups containing the mentionedprecursors. The average precursors’ half-lives, computedusing the new set of abundances, are listed in Tab. XXII,together with the uncertainty calculated with and with-out correlations. b. Comparison with recommended values.
The ki-netic parameters obtained by summation calculationsare compared with those recommended by the CRP inthe 8-group model (see Section IX). The CRP recom-mended values consist of those recommended by WPEC-SG6 (2002) [14], except for the sets of abundances mea-sured by IPPE after 2002 ([226, 228–230]) for which spe-cial recommendations are made in Section IX. The abun-dances ( a i ) and decay-constants ( λ i ) recommended byWPEC-SG6 (2002) were obtained from the expansion of the 6-group parameter set measured by Keepin in 1957,to an 8-group parameter set [14]. In the framework ofWPEC-SG6 [14], it also appeared convenient to fix thedecay-constants for all fissioning systems in order to sim-plify the kinetic calculations involving more than one fis-sioning system.Figures 46 to 49 show the comparison between mea-sured and calculated kinetic parameters. Each figurerefers to one group abundance and compares several fis-sioning systems and energies.From the results it is evident that the calculated abun-dances are affected by larger uncertainties since they re-flect the uncertainties in hundreds of microscopic param-eters. The integral experiment does not consider the un-certainties in the microscopic data explicitly, but rathercaptures the global behavior, which leads to smaller un-certainties on the fitted abundances. Furthermore, thesummation calculations have been performed startingfrom the independent fission yields, which - due to thecomplexity of the measurements - are affected by larger61evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 44. Thermal neutron-induced fission of
U. Left side: comparison of the integral delayed spectra in the time interval 4-44s [243] with corresponding spectra calculated by means of the summation method using different sets of microscopic delayedneutron data. Right side: the integral delayed spectra in the time interval 0.12-1 s. The Greenwood et al. [17, 18] spectra areadded to the ENDF/B-VII.1 data base [24] (irradiation time of experiments - 20 s).TABLE X. Temporal parameters obtained from summation calculations [per 100 fissions], computed using JEFF-3.1.1 fissionyields and CRP+ENDF/B-VIII.0 decay data. Relative uncertainties are given in brackets.Sample a a a a a a a a Th f U f U t U f U f U f Np f Pu t Pu f Pu f Am f uncertainties than the cumulative fission yields. Thecomparison with the experimental values unveils somepatterns between calculated and measured parameters.Depending on the group, the calculated a i is either over-estimated or underestimated, and this is true indepen-dently of the fissioning system or of the energy. The firstabundance is fairly well estimated. The values are veryclose with the recommended data and the uncertaintyranges overlap (see Fig. 46). This is true for all fission-ing system and all energies, suggesting that the long-livedprecursors, such as Br and Rb, are well identified andtheir data are well known. The CRP+ENDF/B-VIII.0database gives a slightly smaller a than ENDF/B-VIII.0,because the P n of Rb has been set to zero. The reasonis that its Q βn happens to be very small and experimen-tal values are still preliminary (see Table XXIII). On theother hand, the ENDF/B-VIII.0 value is adopted from systematics [129].The second abundance, which should only include Iand
Cs, is very well estimated for the fast fission of
Th, while it is badly estimated for the fast fission of
U. For the rest of the fissioning systems and energies,the calculated values always agree with the experimen-tal a within the range of uncertainty. In some cases,ENDF/B-VIII.0 is closer to the recommended value thanCRP+ENDF/B-VIII.0 ( U t , U f , Np f , Pu t , Pu f ). In other cases, however, it is the other wayaround ( U f , U f , Pu f ). The CRP+ENDF/B-VIII.0 a is always slightly larger than the ENDF/B-VIII.0 value, due to the fact that the P n value for I hasbeen increased from 0.0714 to 0.0765 (see Table XXIV).It is evident though, that both libraries slightly under-estimate a . This may indicate that a revision of themicroscopic data of Cs and
I is needed or that the62evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al.
TABLE XI.
Th-fast fission. a i correlation matrix.1 0.068 0.076 0.071 -0.146 -0.124 -0.028 0.0760.068 1 -0.138 0.315 -0.465 -0.206 0.149 -0.0120.076 -0.138 1 -0.224 0.052 -0.149 -0.251 0.1080.071 0.315 -0.224 1 -0.572 -0.299 0.228 -0.042-0.146 -0.465 0.052 -0.572 1 -0.198 -0.665 0.035-0.124 -0.206 -0.149 -0.299 -0.198 1 0.004 -0.209-0.028 0.149 -0.251 0.228 -0.665 0.004 1 -0.2690.076 -0.012 0.108 -0.042 0.035 -0.209 -0.269 1 TABLE XII. U-fast fission. a i correlation matrix.1 -0.088 0.099 -0.178 -0.247 0.157 0.044 0.180-0.088 1 -0.173 -0.025 -0.424 -0.208 -0.013 -0.1400.099 -0.173 1 -0.438 -0.333 0.250 -0.086 0.231-0.178 -0.025 -0.438 1 -0.322 -0.631 0.123 -0.474-0.247 -0.424 -0.333 -0.322 1 0.173 -0.331 0.0550.157 -0.208 0.250 -0.631 0.173 1 -0.252 0.4640.044 -0.013 -0.086 0.123 -0.331 -0.252 1 0.0210.180 -0.140 0.231 -0.474 0.055 0.464 0.021 1TABLE XIII. U-fast fission. a i correlation matrix.1 -0.026 0.161 -0.076 -0.216 0.151 -0.008 0.111-0.026 1 -0.150 -0.067 -0.446 -0.199 -0.060 -0.0980.161 -0.150 1 -0.271 -0.282 0.292 -0.087 0.155-0.076 -0.067 -0.271 1 -0.385 -0.458 -0.012 -0.212-0.216 -0.446 -0.282 -0.385 1 0.053 -0.374 -0.1130.151 -0.199 0.292 -0.458 0.053 1 -0.264 0.139-0.008 -0.060 -0.087 -0.012 -0.374 -0.264 1 0.1020.111 -0.098 0.155 -0.212 -0.113 0.139 0.102 1 TABLE XIV. U-thermal fission. a i correlation matrix.1 -0.041 0.122 -0.087 -0.193 0.133 0.007 0.118-0.041 1 -0.171 -0.134 -0.456 -0.228 -0.042 -0.1070.122 -0.171 1 -0.256 -0.264 0.253 -0.098 0.188-0.087 -0.134 -0.256 1 -0.380 -0.454 0.024 -0.240-0.193 -0.456 -0.264 -0.380 1 0.044 -0.346 -0.0130.133 -0.228 0.253 -0.454 0.044 1 -0.173 0.1870.007 -0.042 -0.098 0.024 -0.346 -0.173 1 -0.0090.118 -0.107 0.188 -0.240 -0.013 0.187 -0.009 1TABLE XV. U-fast fission. a i correlation matrix.1 0.005 0.086 -0.013 -0.156 0.027 -0.047 0.0780.005 1 -0.158 0.025 -0.385 -0.233 -0.012 -0.0460.086 -0.158 1 -0.163 -0.173 0.145 -0.175 0.117-0.013 0.025 -0.163 1 -0.461 -0.382 0.016 -0.109-0.156 -0.385 -0.173 -0.461 1 -0.026 -0.521 -0.070.027 -0.233 0.145 -0.382 -0.026 1 -0.131 -0.062-0.047 -0.012 -0.175 0.016 -0.521 -0.131 1 -0.0960.078 -0.046 0.117 -0.109 -0.07 -0.062 -0.096 1 TABLE XVI. Np-fast fission. a i correlation matrix.1 -0.109 0.165 0.002 -0.18 0.141 -0.006 0.132-0.109 1 -0.211 -0.143 -0.542 -0.236 -0.106 -0.1480.165 -0.211 1 -0.162 -0.244 0.298 -0.081 0.1910.002 -0.143 -0.162 1 -0.303 -0.36 0.019 -0.159-0.18 -0.542 -0.244 -0.303 1 -0.007 -0.311 -0.1110.141 -0.236 0.298 -0.36 -0.007 1 -0.25 0.169-0.006 -0.106 -0.081 0.019 -0.311 -0.25 1 0.1080.132 -0.148 0.191 -0.159 -0.111 0.169 0.108 1TABLE XVII. U-fast fission. a i correlation matrix.1 -0.051 0.179 0 0.021 -0.033 -0.119 0.032-0.051 1 -0.243 0.077 -0.302 -0.288 -0.025 -0.0570.179 -0.243 1 -0.149 0.161 0.029 -0.305 0.0190 0.077 -0.149 1 -0.448 -0.284 0.098 -0.0170.021 -0.302 0.161 -0.448 1 -0.166 -0.572 -0.114-0.033 -0.288 0.029 -0.284 -0.166 1 -0.113 -0.15-0.119 -0.025 -0.305 0.098 -0.572 -0.113 1 -0.270.032 -0.057 0.019 -0.017 -0.114 -0.15 -0.27 1 TABLE XVIII. Pu-fast fission. a i correlation matrix.1 -0.181 0.235 0.048 -0.161 0.231 0.034 0.216-0.181 1 -0.237 -0.241 -0.634 -0.209 -0.145 -0.1840.235 -0.237 1 -0.127 -0.234 0.362 -0.036 0.2720.048 -0.241 -0.127 1 -0.193 -0.297 0.062 -0.152-0.161 -0.634 -0.234 -0.193 1 -0.078 -0.196 -0.1420.231 -0.209 0.362 -0.297 -0.078 1 -0.252 0.3240.034 -0.145 -0.036 0.062 -0.196 -0.252 1 0.2170.216 -0.184 0.272 -0.152 -0.142 0.324 0.217 1TABLE XIX. Pu-thermal fission. a i correlation matrix.1 -0.234 0.201 0.076 -0.069 0.25 0.053 0.229-0.234 1 -0.332 -0.364 -0.648 -0.295 -0.168 -0.2580.201 -0.332 1 0.093 -0.178 0.371 -0.032 0.2860.076 -0.364 0.093 1 -0.186 -0.125 0.024 -0.039-0.069 -0.648 -0.178 -0.186 1 -0.032 -0.076 -0.0760.25 -0.295 0.371 -0.125 -0.032 1 -0.222 0.3880.053 -0.168 -0.032 0.024 -0.076 -0.222 1 0.2240.229 -0.258 0.286 -0.039 -0.076 0.388 0.224 1 TABLE XX. Am-fast fission. a i correlation matrix.1 -0.162 0.025 -0.045 -0.139 0.191 0.04 0.196-0.162 1 -0.211 -0.214 -0.588 -0.187 -0.11 -0.1570.025 -0.211 1 -0.279 -0.296 0.176 -0.088 0.147-0.045 -0.214 -0.279 1 -0.173 -0.398 0.126 -0.302-0.139 -0.588 -0.296 -0.173 1 0.006 -0.15 -0.0610.191 -0.187 0.176 -0.398 0.006 1 -0.263 0.4990.04 -0.11 -0.088 0.126 -0.15 -0.263 1 0.1730.196 -0.157 0.147 -0.302 -0.061 0.499 0.173 1TABLE XXI. Pu-fast fission. a i correlation matrix.1 -0.1 0.205 0.021 -0.148 0.19 -0.02 0.129-0.1 1 -0.262 -0.264 -0.504 -0.242 -0.139 -0.1420.205 -0.262 1 0.091 -0.267 0.346 -0.098 0.1740.021 -0.264 0.091 1 -0.316 -0.221 -0.058 -0.088-0.148 -0.504 -0.267 -0.316 1 -0.103 -0.231 -0.1250.19 -0.242 0.346 -0.221 -0.103 1 -0.209 0.109-0.02 -0.139 -0.098 -0.058 -0.231 -0.209 1 0.0680.129 -0.142 0.174 -0.088 -0.125 0.109 0.068 1 . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
TABLE XXII. Average half-lives (cid:104) T (cid:105) and uncertainties forfast (f) and thermal (t) neutron-induced fission of minor andmajor actinides.Nuclide (cid:104) T (cid:105) [s] σ (no corr.) [%] σ (corr.) [%] Th f U f U t U f U f U f Np f Pu t Pu f Pu f Am f -1-0.8-0.6-0.4-0.200.20.40.60.81 FIG. 45. Group abundances correlation matrix for severalfissioning systems and energies. The correlations are producedby the CONRAD code through an analytical marginalizationtechnique. fission yields need to be investigated.The third abundance, which should only include
Teand Br, is very well estimated for the thermal fissionof
U and the fast fission of
Pu, while it is badlyestimated for the fast fission of
Th. For the rest ofthe fissioning systems, it seems that the ENDF/B-VIII.0
TABLE XXIII. Precursors contributing to the first delayedneutron groupIsotope Quantity ENDF/B-VIII.0 CRP+ENDF/B-VIII.0 Rb P n [-] 2.0319E-07 0T / [s] 58.40 57.90 Br P n [-] 0.026 0.0253T / [s] 55.65 55.64 Th f 233 U f 235 U t 235 U f 236 U f 238 U f 237 Np f239 Pu t239 Pu f241 Pu f a RecommendedComputed - ENDF/B-VIII.0Computed CRP+ENDF/B-VIII.0 Th f 233 U f 235 U t 235 U f 236 U f 238 U f 237 Np f239 Pu t239 Pu f241 Pu f a RecommendedComputed - ENDF/B-VIII.0Computed CRP+ENDF/B-VIII.0
FIG. 46. First and Second group abundances for several fis-sioning systems and energies. Comparison between summa-tion calculation results and recommended values. The uncer-tainty in the calculated abundances is obtained through ananalytical marginalization technique.TABLE XXIV. Precursors contributing to the second delayedneutron groupIsotope Quantity ENDF/B-VIII.0 CRP+ENDF/B-VIII.0 Cs P n [-] 0.00035 0.00034T / [s] 24.84 24.91 I P n [-] 0.0714 0.0763T / [s] 24.50 24.59 a values are always closer to the experimental valuesthan the CRP. The differences between the two librariesare reported in Tab. XXV and concern the Te half-lifeand Br branching ratio P n . However, for both libraries,the general trend is a slight underestimation of a withrespect to experiments.Both ENDF/B-VIII.0 and CRP+ENDF/B-VIII.0 con-verge towards the same largely underestimated a . Theonly actinides for which the parameter is fairly well es-timated are Th f , U f , U f and Pu f . On theother hand, U t , U f , and Np f are very far fromthe recommended values.Figures 48 and 49 show that the estimation of the64evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al. Th f 233 U f 235 U t 235 U f 236 U f 238 U f 237 Np f239 Pu t239 Pu f241 Pu f a RecommendedComputed - ENDF/B-VIII.0Computed CRP+ENDF/B-VIII.0 Th f 233 U f 235 U t 235 U f 236 U f 238 U f 237 Np f239 Pu t239 Pu f241 Pu f a RecommendedComputed - ENDF/B-VIII.0Computed CRP+ENDF/B-VIII.0
FIG. 47. Third and Fourth group abundance for several fis-sioning systems and energies. Comparison between summa-tion calculation results and recommended values. The uncer-tainty in the calculated abundances is obtained through ananalytical marginalization technique.TABLE XXV. Precursors contributing to the third delayedneutron groupIsotope Quantity ENDF/B-VIII.0 CRP+ENDF/B-VIII.0 Te P n [-] 0.0131 0.0137T / [s] 17.50 17.67 Br P n [-] 0.0658 0.0672T / [s] 16.29 16.29 short-lived precursors’ abundances needs improvement.The fifth abundance which includes precursors Rb, I, As and m Y, is systematically overestimated with theexception of some isolated cases ( U f and Th f ). Onthe other hand, the seventh abundance, which involves Br and Rb, is systematically underestimated, withthe exception of U f and Np f . The sixth and eightabundances do not follow any specific pattern. It shouldbe stressed that these results and conclusions are depen-dent upon the FY dat used to calculate the DN activ-ity, and could be different if a different FY library wasadopted. Th f 233 U f 235 U t 235 U f 236 U f 238 U f 237 Np f239 Pu t239 Pu f241 Pu f a RecommendedComputed - ENDF/B-VIII.0Computed CRP+ENDF/B-VIII.0 Th f 233 U f 235 U t 235 U f 236 U f 238 U f 237 Np f239 Pu t239 Pu f241 Pu f a RecommendedComputed - ENDF/B-VIII.0Computed CRP+ENDF/B-VIII.0
FIG. 48. Fifth and Sixth group abundance for several fission-ing systems and energies. Comparison between summationcalculation results and recommended values. The uncertaintyin the calculated abundances is obtained through an analyti-cal marginalization technique. c. Effect of the abundances set on the quantities ofinterest.
In this paragraph,the effect of the abundancessets on quantities of interest, such as the mean delayedneutron half-life and the delayed neutron activity, is dis-cussed. Table XXVI shows the average half-life values (cid:104) T (cid:105) computed using different sets of DN abundances. In par-ticular, (cid:104) T (cid:105) values obtained using ENDF/B-VIII.0 andCRP+ENDF/B-VIII.0 decay data are compared withrecommended values for the fast neutron-induced fissionof U, U, Pu and the thermal-induced fission of U, Pu. The average half-life of DN precursors ob-tained by summation calculations has larger uncertaintiesthan the recommended ones, due to the marginalizationof hundreds of microscopic input data. Correlations havenegligible effect on the uncertainty since they account forapproximately 1% of the total uncertainty. The meanhalf-lives for
Pu (thermal),
U (thermal) and
U(fast) are well estimated. On the other hand, the re-sults for
U (fast) and
Th (fast) deviate from themeasured values therefore the relevant microscopic nu-clear data require significant improvement. For the otherisotopes and energies, the results are rather satisfactory,65evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al. Th f 233 U f 235 U t 235 U f 236 U f 238 U f 237 Np f239 Pu t239 Pu f241 Pu f a RecommendedComputed - ENDF/B-VIII.0Computed CRP+ENDF/B-VIII.0 Th f 233 U f 235 U t 235 U f 236 U f 238 U f 237 Np f239 Pu t239 Pu f241 Pu f a RecommendedComputed - ENDF/B-VIII.0Computed CRP+ENDF/B-VIII.0
FIG. 49. Seventh and Eight group abundance for several fissioning systems and energies. Comparison between summationcalculation results and recommended values. The uncertainty in the calculated abundances is obtained through an analyticalmarginalization technique. even though further work is needed to reduce the ob-served disagreement with recommended data.
TABLE XXVI. Average half-lives (cid:104) T (cid:105) and uncertainties com-pared with measured values for fast (f) and thermal (t)neutron-induced fission of minor and major actinides pre-sented in Tables XXXVII-XXXVIII.Nuclide CRP+ENDF/B-VIII.0 ENDF/B-VIII.0 Measured U f ± ± ± U t ± ± ± U f ± ± ± Pu t ± ± ± Pu f ± ± ± Figure 50 shows the DN activity obtained using the cal-culated set of a i versus the delayed neutron activity ob-tained using the measured set of a i . The plotted quantityis the ratio of the two activities. The graph is composedof several curves, each representing a different fissioningsystem or a different incident neutron energy. The behav-ior of the ratio reflects the differences in the group abun-dances. The recommended set of abundances is expectedto reproduce the measured DN activity fairly well, so thecomparison with the calculated one reflects the quality ofthe nuclear data. From the figure, it appears that, withthe current microscopic data, it is possible to perfectlyestimate the DN activity for the thermal fission of U.The same is not true for other fissioning systems or en-ergies, where the discrepancies can reach up to 20% (see Th f or Pu f ). Since the activity is represented by asum of exponentials of the abundances, it is expected tobe highly sensitive to small variations in the abundances.The asymptotic value of the ratio between the activitiesis directly linked to a , which is, in principle, fairly wellestimated. As far as Pu f is concerned, the calculated a is 0.013, while the recommended one is 0.016. Sucha small difference is responsible for the 20% difference inthe DN activity. To conclude, in this section we attempted to verify thequality of the new microscopic CRP data ( T / , P n ) byextracting 8-group parameters ( a i , λ i ) from the DN ac-tivity obtained from summation calculations over thesedata. The first abundance is fairly well estimated for allfissioning systems and energies, while the others dependstrongly on the case under investigation. A pattern seemsto emerge in the systematic overestimation of a and un-derestimation of a , implying that precursors belongingto the fifth ( Rb, I, As and m Y) and seventh group( Br and Rb) may need to be revisited. Abundancecorrelation matrices have been obtained and used in theestimation of the uncertainty of quantities of interest, like (cid:104) T (cid:105) . Although the correlations appear to be weak, theirconsideration in the estimation of the total uncertaintyof (cid:104) T (cid:105) is important. In spite of the discrepancies ob-served between calculated and measured a i , the averagehalf-lives are comparable while the large underestimationobtained for U (fast) and
Pu (fast) suggests that toomuch weight is assigned to short-lived precursors in thefast neutron-induced fission. As far as the DN activityis concerned, the current microscopic data are not ableto reproduce the experimental curve for all fissioning sys-tems and energies. Figure 50 shows that the discrepancycan reach ±
20% for Pu f and U f , while U t is per-fectly reproduced. One should bear in mind though, thatthe reactivity, which is the quantity of interest for reactorphysicists, is less sensitive to the abundances than the ac-tivity. Therefore, a 20% discrepancy in the DN activitydoes not necessarily translate into a similar discrepancyin the reactivity. Rather, 300 s after irradiation, the lat-ter has a tendency to depend on the mean half-life of theprecursors.On the other hand, one should bear in mind that the re-sults for the time-dependent parameters depend not onlyon the microscopic decay data but also on the FY librarythat was used. Therefore, apart from revisiting certaindecay data ( T / , P n ) as suggested from the comparisonof abundances, it is also crucial to review and improve the66evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al. -3 -2 -1 Time after irradiation [s] n d , CR P / n d , R e c o mm ended Th f233 U f235 U t235 U f 236 U f238 U f237 Np f239 Pu t 239 Pu f241 Pu f FIG. 50. Delayed neutron activity ratio for several fissioning systems and energies. The CRP activity has been computed usingthe abundances derived from the summation calculation using CRP decay data ( T / , P n ). The Recommended activity has beenobtained by using the recommended sets of abundances. existing evaluated FY libraries before any final conclusioncan be drawn on the CRP β -delayed neutron emissiondata. VII. INTEGRAL CALCULATIONS
In Sect. VI, summation calculations were used to de-termine the total delayed neutron yields from fission asa function of the incident neutron energy ν d (E). More-over, they were used to check the consistency of the new( T / , P n ) data through systematic comparisons with rec-ommended values. In this section, we attempt to validatethe new CRP ( T / , P n ) data by studying their impacton specific reactor designs and comparing their resultsagainst well-measured benchmark experiments. A. Comparison with integral experiments
The first step in the comparison with integral experi-ments was to perform summation calculations of ν d (E)using the following combinations of input data fromENDF/B-VIII.0 [25] and JEFF-3.3 [29] evaluated nucleardata libraries, and the new CRP P n tables: i) fissionyields and decay data from the same nuclear data library(v01); ii) fission yields from nuclear data libraries andCRP P n values complemented with decay data from thesame library (v02); iii) JEFF-3.3 fission yields and decaydata form ENDF/B-VIII.0 (v03); and iv) JEFF-3.3 fis- sion yields and CRP P n values complemented with datafrom ENDF/B-VIII.0 decay library (v04) which is identi-cal to CRP+ENDF/B-VIII.0 from the previous sections.In the following, these calculated ν d values will be re-ferred to as modified ν d , while the recommended ν d con-tained in the evaluated nuclear data libraries will be re-ferred to as recommended . Differences between 5% and10% can be found between recommended JEFF-3.3 andENDF/B-VIII.0 ν d values. Furthermore, recommended ν d and modified ν d values differ by up to 70% in somecases. An example of this behaviour can be seen in Fig-ure 51 for U.To validate the CRP ( T / , P n ) data, the ν d valuesobtained from the above-mentioned summation calcula-tions have been used in simulations of integral experi-ments from the International Criticality Safety Bench-mark Evaluation Project (ICSBEP) Handbook [276] us-ing the MCNP 6.1.1 code [277]. Integral benchmarks con-sist of extensively peer-reviewed data that can be used bythe international nuclear data community for testing andimprovement of nuclear data files. They are also used bythe international reactor physics, criticality safety, andmath & computation communities for validation of ana-lytical methodologies used for reactor physics, fuel cycle,nuclear facility safety analysis and design, and advancedmodeling and simulation efforts [278].For our purposes, we have chosen 9 integral exper-iments with available measured effective delayed neu-tron fraction β eff : POPSY, TOPSY, JEZEBEL, SKI-DOO and FLATTOP-23, which all have a simple spher-67evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al. -5 -3 -1 Incident neutron energy (eV) ν d U ENDF/B-VIII.0
U JEFF-3.3
U JEFF-3.3 v01
U ENDF/B-VIII.0 v02
FIG. 51. Comparison between recommended and modifieddelayed neutron yields for U. ical geometry; and in addition, BIG TEN, SNEAK-7A,SNEAK-7B and IPEN, all of which have a reactor-typeconfiguration. The IPEN integral experiment is the onlyone based on a thermal spectrum, whereas the rest ofthem are fast spectrum systems.According to Keepin [279], the effective delayed neu-tron fraction is defined as the ratio between the adjointweighted delayed ( P d,eff ) and total ( P eff ) neutron pro-duction: β eff = P d,eff P eff (29)with: P eff = (cid:90) φ ∗ ( (cid:126)r, E (cid:48) , Ω (cid:48) ) χ ( E (cid:48) ) ν ( E )Σ f ( (cid:126)r, E ) φ ( (cid:126)r, E, Ω) δEδ Ω δE (cid:48) δ Ω (cid:48) δ(cid:126)r (30) P d,eff = (cid:90) φ ∗ ( (cid:126)r, E (cid:48) , Ω (cid:48) ) χ d ( E (cid:48) ) ν d ( E )Σ f ( (cid:126)r, E ) φ ( (cid:126)r, E, Ω) δEδ Ω δE (cid:48) δ Ω (cid:48) δ(cid:126)r (31)where φ ( (cid:126)r, E, Ω) and φ ∗ ( (cid:126)r, E (cid:48) , Ω (cid:48) ) are the direct andadjoint angular fluxes, χ ( E (cid:48) ) is the energy spectrum ofthe generated fission neutrons, ν ( E ) is the average neu-tron multiplicity per fission. Correspondingly, χ d ( E (cid:48) )and ν d ( E ) are the same quantities but for delayed neu-trons and Σ f ( (cid:126)r, E ) is the macroscopic fission cross sectionof the material. β eff has been selected as reference in-tegral parameter since the sensitivity of β eff to changesin delayed neutron data is significantly greater than toother data [280].A sensitivity analysis was carried out first with theSUMMON [281] code to identify the main fissioning sys-tems contributing to β eff in each integral experiment. P O P S Y T O P S Y B I G T E N J E Z E B E L S N E A K A S N E A K B S K I D O O F L A T T O P I P E N C / E β e ff P u / U U U / U P u P u / U U / P u U U / U U Exp. dataENDF/B-VIII.0ENDF/B-VIII.0 V01ENDF/B-VIII.0 V02ENDF/B-VIII.0 V03ENDF/B-VIII.0 V04 P O P S Y T O P S Y B I G T E N J E Z E B E L S N E A K A S N E A K B S K I D O O F L A T T O P I P E N C / E β e ff P u / U U U / U P u P u / U U / P u U U / U U Exp. dataJEFF-3.3JEFF-3.3 V01JEFF-3.3 V02JEFF-3.3 V03JEFF-3.3 V04
FIG. 52. C/E comparison with the recommended and modi-fied ν d values from ENDF/B-VIII.0 (top) and JEFF-3.3 (bot-tom) for the 9 integral experiments. The results are presented in Table XXVII. Although someexperiments are characterized by a major contribution to β eff coming from a single isotope, such as JEZEBEL, inothers such as BIG TEN, we observe nearly equal contri-butions coming from two isotopes. In the latter case, itis difficult to assess the impact of ν d changes in β eff dueto compensation effects.The next step was to perform the simulations using anadequate number of particle histories to achieve negligiblestatistical uncertainties ( < β eff . The resultsof the simulations are shown in Fig. 52, where the top x-axis shows the isotopes which are the main contributorsto β eff for each integral experiment (see Table XXVII).The β eff results obtained with the recommendedENDF/B-VIII.0 ν d values are in reasonable agreementwith the experiments. Good agreement is also observedfor the recommended JEFF-3.3 ν d values. Regarding theDN yields obtained from the summation calculations, thev01 values obtained from JEFF-3.3 severely underesti-mate β eff in most of the cases. Since this is the only68evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
TABLE XXVII. Relative contributions of main isotopes to the β eff for every integral experiment.Integral exp. Relative contribution to β eff Brief descriptionPopsy 52.5%
Pu, 40.9%
U Pu core, U-nat reflectorTopsy 72.7%
U, 25.4%
U HEU core, U-nat reflectorBig Ten 52.8%
U, 46.6%
U U cylindrical shape coreJezebel 90.9%
Pu, 7.1%
Pu Pu bare sphereSneak 7A 46.1%
Pu, 45.2%
U MOX coreSneak 7B 51.9%
U, 38.5%
Pu MOX coreSkidoo 97.2%
U, 1.3% U U bare sphereFlattop-23 65.7%
U, 30.3% U U core, U-nat reflectorIpen 88.8%
U, 11.1%
U UO core (thermal) combination of JEFF-3.3 FYs that gives such large devi-ations, it is very likely that the source of these deviationsis the JEFF-3.3 decay data library. On the contrary, thev01 values derived from ENDF/B-VIII.0 agree with sixout of the nine experimental results. In the remainingthree cases, which are the ones where the main contrib-utor to β eff is U, an overestimation is observed. Ofall the summation combinations using ENDF/B-III.0 li-braries, v02 and v03 which use ENDF/B-VIII.0 FYs arethe most discrepant, so it is most likely that the latterENDF/B-VIII.0 FYs do not perform that well. The com-bination of fission yields from JEFF-3.3 and decay datafrom ENDF/B-VIII.0 (v03) gives overall good agreementwith the experimental results which is comparable to therecommended data. Finally, when the ENDF/B-VIII.0decay P n data in v03 are replaced by the new CRP P n data to form v04, the agreement is not improved insteadit is slightly worsened as we observe an increase in the re-spective β eff . Overall, we find that the CRP P n data leadto an increase in β eff with respect to the β eff obtainedwhen using the two other decay data libraries. Note thatthe modified decay-data libraries (v03) and (v04) give dif-ferent results when used with ENDF/B-VIII.0 and JEFF-3.3 cross-section libraries, as seen in the upper and lowerpanels of Fig. 52, respectively.We have shown that the summation technique is a use-ful tool for calculating ν d values that can reproduce reac-tor parameters with acceptable accuracy. This is partic-ularly relevant for the minor actinides, for which no ex-perimental fission pulse data are available, but for whichfission yields and decay data are available. On the otherhand, the use of the new CRP data in integral calcula-tions results in increased values of β eff , at least for the9 benchmark experiments studied herein. These resultsagree with the findings of the previous section (Sect. ?? )and confirm the need to investigate the evaluated fissionyield libraries before conclusions are drawn with respectto the β -delayed neutron data. B. Impact on reactor calculations
The impact of the new CRP data on reactor calcula-tions has also been assessed by performing two different analyses described in this section. a. Analysis I.
A pressurized water reactor (PWR)and two GEN-IV fast reactor concepts have been selectedin this first analysis: a pin design (with reflective bound-ary surfaces) representative of the Obrigheim PWR [282],the sodium cooled ASTRID (Advanced Sodium Tech-nological Reactor for Industrial Demonstration) reac-tor [283] and the lead-bismuth cooled MYRRHA (Multi-purpose hYbrid Research Reactor for High-tech Applica-tions) reactor [284].Calculations of β eff were performed using the modi-fied libraries (v01-v04), as well as recommended libraries,described in Sect. VII. Results from these calculationsare presented in Table XXVIII, where statistical uncer-tainties of the order of 4% in β eff have been neglected.The β eff values obtained with the modified libraries de-viate from those obtained using the recommended ν d data by up to ∼
10% in ASTRID and MYRRHA forboth ENDF/B-VIII.0 and JEFF-3.3 libraries. This isin agreement with the differences observed in the inte-gral experiment calculations presented in the previousSect. VII. Regarding the PWR model, for JEFF-3.3 thelargest difference observed is again ∼ ∼
44% (v02). This result agrees with the findings for theIpen experiment (the only one with thermal spectrum)discussed in the previous section which showed larger de-viations with respect to the recommended values whenusing the ENDF/B-VIII.0 library combinations.To conclude, similar to the results of β eff obtained inthe previous section, we find that the best combinationof input data is v03 with JEFF-3.1.1 FYs and ENDF/B-VIII.0 decay data. When the ENDF/B-VIII.0 P n dataare replaced with the CRP values (v04), the agreementis slightly worsened except for one case, the PWR JEFF-3.1.1 recommended value. The deviations with respectto recommended data increase when the ENDF/B-VIII.0FY library or the JEFF-3.1.1 decay data library is usedin the combination. b. Analysis II. In the second analysis, a Sodium FastBreeder reactor (FBR) model has been used to computethe β eff with MCNPX2.6.f coupled to an evolution codewithin the MCNP Utility for Reactor Evolution (MURE)software [274]. The model is extracted from [285] and thesimulation has been originally developed for the study69evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
TABLE XXVIII. Calculated effective delayed neutron frac-tion values for PWR, ASTRID and MYRRHA reactors usingrecommended and modified libraries.PWRENDF/B-VIII.0 JEFF-3.3 β eff Relative to rec. β eff Relative to rec.rec. 657 - 695 -v01 843 1.28 620 0.89v02 945 1.44 728 1.05v03 667 1.02 666 0.96v04 704 1.07 685 0.99ASTRIDENDF/B-VIII.0 JEFF-3.3 β eff Relative to rec. β eff Relative to rec.rec. 344 - 338 -v01 348 1.01 316 0.93v02 361 1.05 342 1.01v03 339 0.99 343 1.01v04 305 0.89 367 1.09MYRRHAENDF/B-VIII.0 JEFF-3.3 β eff Relative to rec. β eff Relative to rec.rec. 319 - 321 -v01 337 1.06 299 0.93v02 355 1.11 332 1.03v03 321 1.01 321 1.00v04 326 1.02 317 0.99 of the anti-neutrino emission from a sodium FBR (Na-FBR). Several versions of the model associated with vari-ous fuel compositions were used. The detailed descriptionof the model can be found in [286], here we present onlythe information necessary for understanding the presentresults.In the FBR model, a central zone corresponds to the in-ternal core, which is enriched at 21% in plutonium, whilethe external core is enriched at 28% in plutonium, whileaxial and radial blankets surround the core. A set ofassemblies made of stainless steel surrounds the wholeconfiguration, acting as a reflector.The core composition in its internal and external partsis given in Table XXIX. The isotopic plutonium vectorcorresponds to that of the Monju reactor [286]. ThisMixed Oxide fuel (MOX) has a density of 11 g/cm . TABLE XXIX. Fuel composition in the internal and externalcores of the sodium Fast Breeder model reactor (FBR) whichare enriched by 21% and 28% in plutonium, respectively.Isotope Internal Core External core
U 0.79 0.72
Pu 0.1218 0.1624
Pu 0.0504 0.0672
Pu 0.0294 0.0392
Pu 0.0084 0.0112
The composition of the radial and axial blankets is
TABLE XXX. Composition in Minor Actinides (MA) of thetransmutation blanket surrounding the cores of the FBRmodel reactor used in the calculations.Nuclei % weight of Minor Actinides
Cm 0.001
Cm 0.01
Cm 0.4
Cm 0.17
Cm 0.06
Cm 0.01
Cm 0.002
Am 10.4 m Am 0.4
Am 2.9
Np 3.5other 0.001 typical for transmutation. 79% of depleted uranium ex-tracted from CANDU used fuel and 21% of actinides aremixed according to the table XXX.With regards to the depleted uranium composition, theisotopic composition of a depleted plutonium/uraniumvector extracted from a CANDU reactor at 6.7GWd/twas used as simulated. This composition does not ac-count for the decay of
Pu of half-life 14.33 yrs [28].The fuel temperature is 1500 K.A Protected-Plutonium-Production version of the fuelcomposition has been used as well (called ”Fuel 2”), inwhich a significant fraction of
Pu is added to the plu-tonium vector in order to prevent fuel diversion. Thefission rates associated with the two fuel compositionsare displayed in table XXXI.The β eff was extracted at the beginning of the cy-cle. Two methods were used. In the first method, β eff was extracted using the fission rate of each actinide ob-tained from the reactor model combined with the rec-ommended delayed and total neutron fractions ν t,d fromthe JEFF3.1 database [28]. In the second method, thesummation method was used, whereby the fission prod-uct activities obtained in the various simulations usingJEFF-3.1.1 fission yields and JEFF-3.1 decay data werecoupled to the new CRP P n data.Table XXXI shows the results of the computed β eff asa function of the loaded fuel.The β eff values obtained with both methods are dis-played in the two bottom lines of Table XXXI. One cansee that the CRP results are in very good quantitativeagreement with the results using recommended JEFF-3.1.1 ν d values for both fuels, with a difference of lessthan 10 pcm. The β eff value obtained for fuel 1 is largerthan for fuel 2 because of the larger fission rate of P u in the former fuel compared to the latter.This is due tothe added fraction of
P u in fuel 2, which has a verylow ν d .The results confirm the findings of Analysis I showing70evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
TABLE XXXI. Fission rates at the beginning of the cyclecorresponding to the two fuels loaded in the FBR model, andcorresponding β eff (pcm) obtained with the recommendedJEFF-3.1 decay data (JEFF) and the CRP P n data.Nuclides % fission rate % fission rateFuel 1 Fuel 2 U 12.29 12.25
Pu 59.15 54.28
Pu 6.68 3.48
Pu 18.73 12.23
Pu 0.83 0.72
U 0.30 0.30
U 0.00 0.00
Pu - 14.75
Cm 0.02 0.02
Cm 0.03 0.03
Cm 0.06 0.06
Cm 0.43 0.43
Cm 0.01 0.01
Cm 0.02 0.02
Cm 0.00 0.00
Am 0.91 0.91
Am 0.02 0.02
Am 0.19 0.16
Np 0.34 0.34 β eff (JEFF) 471 437 β eff (CRP) 478 447 that the combination of JEFF-3.1.1 FYs with the CRP P n data yields overall good results for β eff which arecomparable to the recommended values. However, thereis an obvious trend that has been observed in all the pre-vious integral calculations, and that is that the CRP P n data yield larger ν d values and subsequently, larger β eff values. Possible culprits for this increase have been sug-gested to be I and Br based on the comparison ofthe corresponding P n data in Sect. VI B 1. However, dueto compensation effects from the variations of P n valuesof several important contributors and the dependence ofthese results on the fission yield library used in the sum-mation calculations, it is not straightforward to draw adefinitive conclusion on the impact of the new CRP data. VIII. SYSTEMATICS OF MACROSCOPICDATA: TIME-DEPENDENT PARAMETERSA. New approach for estimation of temporaryparameters for unmeasured nuclides
The systematics of the delayed neutron (DN) charac-teristics and their correlation properties gives valuable in-formation for developing a reliable database of DN data.The total delayed neutron yields ν d are represented by anexponential function of the parameters involving the mass A c and the atomic numbers Z of the compound fission- ing nucleus ( A c , Z ) [227]. Moscati and Goldemberg [287]proposed the exp [ − K · (2 · Z − N )] dependence whichwas modified to exp [ − K · (3 · Z − A c )] by Caldwell andDowdy [288] and then investigated in detail by Pai [289],Waldo and co-workers [207] and Ronen [290]. The param-eterization − ( A c − · Z ) · ( A c /Z ) has been used by Tuttle[249] along with the experimental data in the evaluationof the total DN yields for the isotopes Pa, U, U, Pu,
Pu,
Pu and
Pu. The systematics of thetemporal DN parameters became possible after introduc-ing in practice the value of the average half-life (cid:104) T (cid:105) of DNprecursors [227]. The (cid:104) T (cid:105) value can be calculated usingexpression (cid:104) T (cid:105) = N (cid:88) i =1 a i · T i , N (cid:88) i =1 a i = 1 , (32)where a i and T i is the relative abundance and the half-life of the i -th DN group, respectively; N the numberof DN groups. When calculating this value on the basisof the microscopic DN data and fission yield data thefollowing expression is used (cid:104) T (cid:105) = (cid:80) Ni =1 CY i · P ni · T / i (cid:80) Ni =1 CY i · P ni , (33)where CY i is the cumulative yield of the i-th DN pre-cursor; P ni and T / i the probability of DN emission andthe half-life of the i-th DN precursor, respectively.It turns out that the (cid:104) T (cid:105) data for the isotopes ofone element can be systematized with the help of theexponential dependence using the Tuttle’s parameter – − ( A c − · Z ) / ( A c /Z ), where A c and Z is the mass andthe atomic numbers of the fissioning compound nucleus,respectively [227]. Furthermore it was found that thetotal DN yields ν d and the average half-life values (cid:104) T (cid:105) for isotopes of one element are related to each other bythe dependence ν d = a · (cid:104) T (cid:105) b , a and b being constants.These findings made it possible to show that the ex-ponential dependence of the ν d value on the parameter − ( A c − · Z ) · ( A c /Z ) has essentially an isotopic char-acter [227]. This means that isotopes of each fissionableelement have their own dependence of ν d on the parame-ter − ( A c − · Z ) · ( A c /Z ) that must be taken into accountin the evaluation process especially for the nuclei lying farfrom the valley of β -stability. The properties of the sys-tematic − ( A c − · Z ) · ( A c /Z ) both for the total DN yieldsand the average half-life of DN precursors are discussed indetail in [227]. The systematics of the average half-life ofDN precursors is useful for the validation of the DN groupparameters for the isotopes of Th, U, Pu and Am and theprediction of the average half life of unmeasured isotopesof these elements. But unlike the − ( A c − · Z ) · ( A c /Z )systematics of the total DN yield, this systematics doesnot allow us to predict the average half-life of DN pre-cursors (cid:104) T (cid:105) for isotopes of such elements as Pa, Cm, Cfand others. Below a new approach for the prediction ofthe average half-life of DN precursors and the appropri-71evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 53. The systematics ( A c /Z ) ·
92 of the average half-lifeof DN precursors. The solid line is the approximation of theaverage half-life by expression (cid:104) T (cid:105) = exp [ a + b · ( A c /Z ) · (cid:104) T (cid:105) were taken from the recom-mended data sets ( a i , T i ) [225]. ate set of relative abundances and periods of individualDN groups for unmeasured nuclides is considered. B. The ( A c /Z ) · systematics of the averagehalf-life It has been shown in [255] that the average half-life ofthe DN precursors of all isotopes of heavy nuclides mea-sured in the fast neutron induced fission can be approx-imated by the expression (cid:104) T (cid:105) = exp [ a + b · ( A c /Z ) · A c and Z is the mass and the atomic numbers ofthe fissioning compound nucleus, respectively. As com-pared with the systematics − ( A c − · Z ) · A c /Z [227],which is valid for isotopes of one element, the system-atics ( A c /Z ) ·
92 allows to predict the average half-lifefor isotopes of all elements with the help of the onlyone set of constants a and b . In Fig. 53 the values ofthe average half-life calculated on the basis of the rec-ommended experimental data ( a i , T i ) for the fast neu-tron induced fission of U, Pu, Am, Np and Th iso-topes [225] are shown by separate points. The solid lineis the approximation of these data by the dependence (cid:104) T (cid:105) = exp [ a + b · ( A c /Z ) · a = 41 . ± . b = − . ± . (cid:104) T (cid:105) de-pendence has a fine structure that is due to the differ-ences in the dependences observed for U, Pu, and Amelements. So for example the coefficients a and b for the (cid:104) T (cid:105) = exp [ a + b · ( A c /Z ) ·
92] dependence for uraniumisotopes are 41.219 ± ± C. Systematics ( A c − · Z ) of relative abundances inthe 8-group model In practice, the time parameters of DN are representedby such characteristics as the relative yields and the pe-riods of individual DN groups. Therefore, the develop-ment of the systematics of the relative yields and peri-ods of DN for individual groups is required. This taskcannot be performed using the 6-group model, becauseof the strong correlation of the periods and the relativeabundances of DN. Until now the only method for predic-tion of the temporary characteristics ( a i , T i ) of DN wasbased on the summation calculations [187]. The 8-groupmodel should be used for the systematics of the relativeabundances because in this representation of the groupparameters there is no correlation between the relativeabundances and periods of DN, and the values of DN pe-riods are universal for the isotopes of all the elements.To estimate the relative abundances of delayed neutronsfrom the fast neutron induced fission of the uranium iso-topes the parameter ( A c − · Z ) was used. In Figs. 54and 55 the 8-group relative abundances of uranium iso-topes a i · ( i = 1 , . . . ,
8) are approximated by expression a i = exp [ c i + b i · ( A c − · Z )], where c i , b i are constants.These constants are estimated for each DN group andthen the obtained dependences a i have been used for thecalculation of the relative abundances of all uranium iso-topes including unmeasured uranium isotopes U and
U. The results of this estimate are presented in Ta-ble XXXII.It can be seen from Table XXXII that the averagehalf-lives (cid:104) T (cid:105) obtained on the basis of the ( A c − · Z )systematics agree both with the recommended data andthe data calculated by the summation techniques withthe exception of the value for U calculated with thehelp of the summation method [187]. These data arealso presented in Fig. 56 from which one can see thatthe predicted values for
U and
U agree with thesystematics ( A c /Z ) · A c /Z ) ·
92 systematics of the average half-life of DNprecursors and the ( A c − · Z ) systematics of the relativeabundances a i have a good predictive power and can beused for the prediction of the temporary DN parametersof unmeasured nuclides. IX. RECOMMENDED DATA IN 6- AND8-GROUP MODELS
In modern nuclear power development programs, pri-ority is given to the development of new concepts of nu-clear reactors characterized by a more stringent energyspectrum of neutrons, a complex composition of nuclearfuel, and the possibility of their use for transmutation ofnuclear waste. Issues such as safety and efficient opera-tion of reactors have increased the need for a reliable andcomplete set of nuclear physical constants used in reac-72evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 54. The ( A c − · Z ) systematics of the relative abundances of delayed neutrons from fission of uranium isotopes (1-4groups). The values of the relative abundances were taken from [224].TABLE XXXII. Relative abundances of uranium isotopes estimated by the ( A c − · Z ) systematics.Uranium isotopes U U U U U U UHalf-life, s Relative abundances, a i (cid:104) T (cid:105) (s) 14.26 12.36 10.68 9.18 7.84 6.63 5.54Systematics ( A c − · Z )Average half-life (cid:104) T (cid:105) (s) 14.60 ± ± ± ± ± ± ± A c /Z ) · (cid:104) T (cid:105) (s) 14.35 ± ± ± ± ± (cid:104) T (cid:105) (s) 14.44 12.36 10.49 7.54 7.77 6.90 5.05summation [187] . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 55. The ( A c − · Z ) systematics of the relative abundances of delayed neutrons from fission of uranium isotopes (5-8groups). The values of the relative abundances were taken from [224]. . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 56. The ( A c /Z ) ·
92 systematics of the average half-life ofDN precursors for uranium isotopes. Full circles - the averagehalf-life of uranium isotopes (recommended data), triangles -the average half-life estimated with the help of ( A − · Z )systematic, squares - the average half-life calculated by thesummation method [187], solid line - the approximation of theaverage half-life by expression (cid:104) T (cid:105) = exp [ a + b · ( A c /Z ) · tor practice, including the database on delayed neutrons(DN).Since the latest recommendations by WPEC-SG6, i.e.the DN group parameters based on the experimental datapresented in [224, 225], a number of measurements of theDN group parameters has been performed at IPPE (Ob-ninsk) for neutron induced fission of uranium, plutonium,thorium, americium, and neptunium isotopes for neutronenergies ranging from thermal to 18 MeV. The short re-view of these data can be found in Section V of this re-port. The compilation of these data is included in thedatabase created within the IAEA Coordinated ResearchProject [41]. There is an increasing need for reliable DNdata uncertainties, including information on the covari-ance matrix of the DN group parameters. The task ofestimating the DN group parameters (the relative abun-dances a i and the half-life T i of their precursor) has be-come more pressing due to the availability of new exper-imental data and current trends in nuclear technologies.In reactor physics practice two models of the DN groupparameters are used: the unconstrained 6- and con-strained 8-group model [224, 225]. In the former, therelative abundances a i and the half-life T i of the individ-ual DN groups are obtained from analysis of the decaycurves of the DN activity by the least-squares method(LSM) with 12 free parameters ( a i , T i ) [13, 226]. In the8- group model the set of the group half-lives T i is uni-versal for all nuclides and primary neutron energies. The T i values of this data set are presented in Table XXXIII.The motivation for the development of the 8-groupmodel and the resulting advantages, as compared withthe 6-group model, are discussed in detail in [224, 225] and include: a significant reduction in the cross correla-tion of the DN group parameters, a more simple dynamicmodel for generating DN in a multi-component mixture offissile nuclides, an improved procedure for the estimationof the DN group energy spectra and a better descriptionof the relationship between reactivity and periods for neg-ative values of reactivity. In the present evaluation therecommended sets of DN group parameters are given in6- and 8-group representation for all nuclides under con-sideration. a. Analysis of the relative abundances and half-livesof delayed neutrons. The selection of the DN decaycurve and the corresponding set of the temporal DN pa-rameters has been carried out on the basis of the timeof the sample transfer from an irradiation position to theneutron detector, the time of recording the decay curve ofDN neutron activity, the number of DN groups resolvedin the experiment, the method for estimating the DN pa-rameters (graphical or LSM), the uncertainties of the DNparameters, the consistency of the DN group parameterswith the systematics of the average half-life of the DNprecursors, and the energy dependence of the temporalDN parameters expressed in the average half-life of theDN precursors [224, 225]. In the present evaluation addi-tional criteria were considered that allow making a wideranalysis of the compared DN data: the ratio of the decaycurves in the 6- and 8-group model to the correspondingrecommended data and the quality of the expansion ofthe 6-group data into the 8-group model. When carryingout this analysis, it was assumed that the 6-group param-eters reproduce the experimental DN decay curve moreaccurately in comparison to the 8-group representation.However, it should be borne in mind that this statementis only valid for the time interval in which these data weremeasured. In the overwhelming number of experimentsthis interval did not exceed 500 s [248]. The aggregateDN curve for each DN data set ( a i , T i ) was modeled inthe range 0-724 s using expression N ( t ) = A · m (cid:88) i =1 (1 − e − λ i · t irr ) · a i · e − λ · t , (34)where A is the saturation activity, t irr the irradiationtime (300 s), ( a i , λ i ) the relative abundance and the de-cay constant of the i -th DN group, m the number of DNgroups. The DN data sets ( a i , T i = ln /λ i ) were takenfrom the compilation by Spriggs and Campbell [248].The 8-group data sets were taken from the evaluationby Spriggs et al. [224, 225] with the exception of the 8-group data sets from the IPPE data obtained after 2002 TABLE XXXIII. Consistent set of half-lives T i in the 8-groupmodel.Group number 1 2 3 4 5 6 7 8Half-life T i (s) 55.6 24.50 16.30 5.21 2.37 1.039 0.424 0.195 . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
TABLE XXXIV. Average half-life of DN precursors (cid:104) T (cid:105) andhalf-life of the first group of DN T in [s] from fission of U, U and
Pu. F is for fast incident neutrons and T forthermal incident neutrons.Target T (cid:104) T (cid:105) T (cid:104) T (cid:105) [13] [226, 230] U F 55.11 ± ± ± ± ± ± ± ± U F 54.51 ± ± ± ± ± ± ± ± Pu F 53.75 ± ± ± ± ± ± ± ± which are not included in the evaluation by Spriggs etal. [225]. A procedure used for the selection of the DNgroup data is shown in the example of the DN data setsmeasured from the thermal and fast neutron induced fis-sion of U, U and
Pu. The DN decay curves ofdifferent authors N ( t ) are presented as the ratio to thecorresponding DN decay curves calculated using the DNsets ( a i , T i ) from the Keepin data N K ) ( t ) [13]. Theobtained data are shown in Figs. 57 and 58.In the interval 0-500 s, the IPPE data [226, 230, 232,235, 250] show the smallest discrepancy with Keepin’sdata [13]. The difference between these data does notexceed 5% for all fissioning systems with the exceptionof the thermal neutron induced fission of Pu. At theend of the considered interval (∆ t = 0-724 s) this differ-ence is increased and reaches 18% for the thermal neu-tron induced fission of Pu. The observed differencebetween decay curves at the end of the considered in-terval is mainly caused by the differences between thehalf-life values of the 1-st DN groups. The half-life val-ues of the 1-st DN group T and the average half-life ofDN precursors (cid:104) T (cid:105) for fission of U, U and
Puare presented in Table XXXIV for both the IPPE andthe Keepin data [13]. Table XXXIV shows that for allfissioning systems the T values in the Keepin data aresystematically lower than the corresponding values of theIPPE data sets. One of the reasons for this may be relatedto the averaging procedure used for the estimation of DNparameters on the basis of different experimental runswhich does not take into account the correlation betweenDN parameters. The second reason for the difference inthe T values is related to the different time intervals inwhich the DN curves were measured. The IPPE tempo-rary DN parameters have been estimated on the basis ofthe experimental data measured in the extended time in-terval (0.12-724 s) [222] while in Keepin’s experiment thisinterval was 500 s. In addition a new averaging procedurefor data sets ( a i , T i ) measured in different experimentalruns has been developed at the IPPE that accounts for acorrelation property of DN group parameters [226, 235].As mentioned above the measurements of the DN decaycurves in [13] have been carried out during 500 s afterthe end of irradiation while in [222, 226] this interval ismuch wider - 724 s. Consequently, the comparison of DN data in the region t >
500 s is not entirely correctsince the Keepin data and data of other authors (witha few exceptions) in this region have been extrapolated because the shape of the DN decay curve here is mainlydetermined by the half-life of the 1-st DN group obtainedfrom data in the range of t <
500 s. In addition, thecomparison of the uncertainty of the DN parameters ofthe 1-st DN group obtained in [13] and [226, 230] showsthat the IPPE data have better statistical accuracy and,most likely, better background conditions. To study theinfluence of interval width used for DN counting on theestimate of the half-life value of the 1-st DN group, theexperimental DN decay curves from the IPPE data [226,230, 255] measured in separate measurement runs fromfission of U, U and
Th by fast neutrons have beenanalyzed in the time intervals 224-714 s, 300-714 s and400-714 s in the frame of a single-group approximation.The results are shown in Table XXXV.It can be seen from Table XXXV that the value for allnuclides in the interval 224 −
724 s is lower than the half-life of Br ( T / = 55 . I ( T / = 24 . Br whichimplies a small contribution of
I activity which in turnmeans that the T / value reaches its asymptotic value.The T / value in the interval 400-724 s has large uncer-tainties because of the low statistics at the end of thedecay curve. The results show that the half-life value ofthe 1-st DN group obtained by the LSM using the 6-groupmodel, can differ significantly from the Br half-life (seethe data for
U in Table XXXV) in spite of the factthat single-group processing of the experimental curve inthe interval 300-724 s gives a value close to the half-life of Br - 55 . ± .
65 s.
Thus, the value of the parametersof the 1-st DN group obtained in the measurements of theDN decay curves is determined not only by the time inter-val in which the measurements are performed, but also bythe peculiarities of the data processing procedure (LSM)and strong cross-correlation between group parameters asit has already been concluded by Spriggs et al. [224, 225].In order to eliminate the disagreement in the DN decaycurves in the range t >
400 s arising from the uncertain-ties in the parameters of the 1-st DN group observed inthe 6-th group model one has to transfer 6-group datato the 8-group model. Figs. 59 and 60 show the ratioof the DN decay curves in the 8-th group representationfrom the IPPE data N ( t ) to the corresponding Keepin8-group data N K ) ( t ) [13] for thermal and fast neutroninduced fission of U, U and
Pu.It can be seen from Figs. 59 and 60 that the discrepancybetween the Keepin and the IPPE data for all consid-ered fissioning systems with the exception of the thermalneutron induced fission of
Pu significantly decreasedand does not exceed 5% in the whole time interval 0-724s. The residual difference in the shape of the DN decaycurves is due to a distinction in the values of the relativeabundances of the 1-st DN group a .76evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 57. The ratio of the DN decay curves in the 6-group representation measured from fission of
U and
U by thermaland fast neutrons to the corresponding DN decay curve calculated using the ( a i , T i ) data sets from Keepin’s data [13]. Thedata references can be taken from the compilation by Spriggs and Campbell [248] except for the data by Piksaikin et al. [226, 230, 235, 250]TABLE XXXV. Half-lives of DN precursors obtained in different time intervals of DN decay curves for the fast neutron inducedfission of Th, U, U.Target nuclides Single-group approximation 6-group approximation [13] 6-group approximation [226, 230, 255]Time interval (s) half-life of half-life ofHalf-life T / (s) 1st DN group T T U 50.72 ± ± ± ± ± Th 53.09 ± ± ± ± ± U 51.24 ± ± ± ± ± This observation as well as the resulting similar val-ues of the average half-life (cid:104) T (cid:105) (see Table XXXIV) canbe considered as the confirmation of the agreement be-tween the IPPE and Keepin data for the fission of Uand
U by thermal and fast neutrons and for the fissionof
Pu by fast neutrons, if they are presented in the8-th group model.
Thus the data presented in Figs.59-60 demonstrate the advantage of the 8-th group model, since it eliminates the discrepancies in the time range t>
400 s associated with uncertainties in determining theparameters of the 1-st DN group within the frameworkof the 6-model.
The divergence in case of the thermalneutron-induced fission of
Pu is caused by a large dif-ference in the relative abundances of the 1-st DN group( a = 0 . ± .
003 and 0 . ± .
001 in the Keepin [13]and the IPPE data [226] sets, respectively). This may be77evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 58. The ratio of the DN decay curves in the 6-group representation measured from the fission of
Pu by thermal and fastneutrons to the corresponding DN decay curve calculated using the ( a i , T i ) data sets from Keepin’s data [13]. The data referencescan be taken from the compilation by Spriggs and Campbell [248] except for the data by Piksaikin et al. [226, 230, 232, 235]FIG. 59. The ratio of the DN decay curves in the 8-group representation from the IPPE data [226, 230, 235, 250] to thecorresponding DN decay curve calculated by using the data sets ( a i , T i ) from the Keepin data [13] measured in the fission of U, U by thermal and fast neutrons. connected to the poor statistics in Keepin’s experimentwhich can be seen seen from the large uncertainties of theaverage half-life of DN precursors observed for the ther-mal neutron induced fission of
Pu: (cid:104) T (cid:105) = 10 . ± .
11s (see Table XXXIV). b. Quality of the expansion method.
Validation ofthe expansion methods [225, 226] used for the transfor- mation of 6-group data to 8-group model data has beenmade on the basis of the ratio of the DN decay curvein the 8-group representation to the corresponding DNdecay curve in the 6-group model. As a result of thiscomparison it has been shown that in the recommendedDN data set [225] the 8-group expanded data and the cor-responding original 6-group data set for the fast neutron78evelopment of a Reference Database . . .
NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 60. The ratio of the DN decay curves in the 8-group representation from IPPE data [226, 230, 232, 235] to the correspondingDN decay curve calculated by using Keepin’s data ( a i , T i ) [13] measured in the fission of Pu by thermal and fast neutrons. induced fission of
U are not consistent. The 8-groupdata set for
U obtained on the basis of the IPPE datahas been proposed as the recommended one. c. High energy data.
The IPPE measurements in thehigh energy range (14-18 MeV) have revealed the possi-ble reasons for the large discrepancy observed in the de-layed neutron temporary parameters: a deterioration ofthe counting property of the neutron detector in a highintensity neutron flux coming from the T(d,n) He reac-tion [239] and the influence of a concomitant D(d,n) Heneutron source generated at an accelerator target in mea-surements using the T(d,n) He reaction [238, 239]. Atpresent, these data are only available in the 6-group rep-resentation. The expansion of these data to the 8-groupmodel will be undertaken in the near future. d. Conclusion.
The efforts undertaken at IPPE forimproving the experimental techniques and data process-ing procedures included the shortening of the transporta-tion time, the extension of delayed neutron counting time,the exact determination of the incident neutron energy aswell as a new approach for averaging the temporary DNparameters obtained in different experimental runs. As aresult, the accuracy of the DN group parameters ( a i , T i )was greatly improved. In general, these studies can beconsidered as the next step following the last evaluationby Spriggs et al. [225] in 2002 leading to the improve-ment of the macroscopic database of the relative abun-dances of delayed neutrons and half-lives of their precur-sors. The revisions introduced to the WPEC-SG6 recom-mended DN temporary data sets [225] are presented inTable XXXVI. A complete set of the present recommen-dations for thermal, fast and high energy fission are givenin Tables XXXVII and XXXVIII. The relative abun-dances and half-lives of delayed neutrons are presentedin the 6- and 8-group model representation with theiruncertainties and the values of the average half-life. In-formation on correlations and covariance matrices can befound in the IAEA compilation database created underthe CRP project [41]. The references for the original 6-group data sets and the 8-group data sets can be foundin the compilation by Spriggs and Campbell [248] and TABLE XXXVI. The revisions made to the WPEC-SG6 rec-ommended sets of temporary DN parameters presented in theevaluation by Spriggs et al. [225]. 6 and 8 stand for 6-groupand 8-group DN parameters, respectively.Neutron energyTarget Thermal Fast High
Th - No revision New (6)
U New (6 & 8) New (6 & 8) No revision
U New (6 & 8) New (6 & 8) No revision
U - New (6 & 8) -
U - New (6 & 8) New (6)
Np - New (6 & 8) New (6)
Pu New (6 & 8) New (6 & 8) New (6)
Am - New (6 & 8) New (6)
Spriggs et al. [224, 225] with the exception of the IPPEdata, the references for which are included in the presentreport.
X. REFERENCE DATABASE
All the compilations, evaluations, systematics as wellas theoretical results and recommendations produced bythe CRP are available on the online Reference Databasefor β -delayed neutron emission [43].The database is split into two parts, the microscopicdata and macroscopic data section. Each section containsa search engine that allows the user to search per nuclide,energy, and in the case of the microscopic database, alsoper ranges of half-lives T / and P n values.All the microscopic data, including compilations, com-ments, and evaluations can be downloaded as Excelspreadsheets while the theoretical results can be down-loaded as ’.csv’ files. The final numerical file of micro-scopic ( T / , P n ) values which is a computer readable filethat has been especially prepared for use in summationcalculations (Sect. VI) and other applications can also bedownloaded as a ’.csv’ file.79evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
In the following, some special features of the two dis-tinct microscopic and macroscopic sections are described.
A. Microscopic data
This database contains all the compiled and evaluatedvalues of T / and P n produced by the CRP evaluatorsand published in [35] ( Z <
29) and [36] (
Z > et al. [129]and [130] but were adapted to the new evaluated data.In addition to the compiled experimental and evalu-ated data, the online database contains theoretical T / and P n values, for comparison. At present, the globalcalculations of Ref. [147] and [153] (see Sect. IV) havebeen included, while more models are planned to be madeavailable in the near future.The online interface provides a search tool which allowsthe user to search in terms of Z, N, A and ranges of half-lives and P n values. The result of the search can also beplotted. Different options for plotting are available (interms of T / , Q β , Q βn , P n ). B. Macroscopic data
The macroscopic database includes three types of ag-gregate data: a. Total delayed neutron yields.
This part containsprevious compilations of measured total delayed neutronyields published in [219–221, 263, 291], as well as newmeasurements performed by the IPPE group [230, 236,259] (see Sect. V A). The data are accompanied by rec-ommendations and comments on necessary adjustments to the data. The whole table including comments can bedownloaded as a .csv file.In addition to the experimental total delayed neutronyields, the user can also retrieve the respective recom-mended yields included in the various evaluated librariessuch as ENDF/B-VII.1 [24], JEFF-3.1.1 [28] and JENDL-4.0 [258]. b. Time-dependent group parameters ( a i , T i ). It in-cludes a compilation of all the time-dependent group pa-rameters measured over the past decades using 4-, 5-,6-, 7- and 8-group models including the new measure-ments performed at IPPE [226, 239, 243] (see Sect. Vand IX). In the case of the latter data, experimental co-variance matrices revealing the correlations between themembers i of the groups are also provided. The recom-mended group parameters of [225] are included as wellas the recommended group-parameters adopted by theevaluated libraries (ENDF/B-VII.1 [24], JEFF-3.1.1 [28]and JENDL-4.0 [258]). c. Composite delayed neutron spectra. A completeset of measured delayed neutron spectra obtained fromRef. [243] (see Sect. V) are contained in this part. Thespectra can be downloaded in numerical tables. Plotscomparing the measured spectra with results of the sum-mation method using the newly evaluated P n values arealso available. XI. SUMMARY AND CONCLUSIONS
In 2019 we celebrated the 80th anniversary of the dis-covery of β -delayed neutrons by Roberts et al. [1, 2]. Thenext generation of radioactive beam facilities that willbecome operational in the next years will allow the ac-cess of even more neutron-rich nuclei in the experimental”Terra Incognita”. This will be a busy time for β -delayedneutron measurements since the vast majority of these3000–4000 still-to-be-discovered nuclides will decay by β -delayed neutron emission. However, the main driver forthese new measurements are no longer fission reactors butthe question how about half of the elements heavier thaniron are created in explosive stellar events like the ”rapidneutron capture ( r ) process” in core collapse supernovaexplosions and binary neutron star mergers [121].The last decade has seen an increased interest in themeasurement of individual nuclear decay properties ofthe most neutron-rich nuclei that can be produced. Theneed for more reliable data for r -process calculations isstrongly intertwined with the better understanding ofthe evolution of single-particle and collective levels inneutron-rich matter.Detection techniques have been developed and im-proved for operation at the next generation of radioac-tive beam facilities, and thoroughly used to map the ex-isting β n-emitter landscape. Worldwide collaborative ef-forts have lead to the discovery of many new neutron-rich isotopes, and the measurement of their half-lives andneutron-branching ratios. The majority of these recent80evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al. T A B L E XXXV II . R e c o mm e nd e d - G r o up D e l a y e d N e u t r o n P a r a m e t e r s , w h e r e T i a nd (cid:104) T (cid:105) i n ( s ) ; ( F ) f o r f a s t n e u t r o n s , ( T ) f o r t h e r m a l n e u t r o n s , ( S F ) f o r s p o n t a n e o u s fi ss i o n . A ll t h e r e f e r e n c e s f o r t h e d a t aa r e i n c l ud e d i n t h e r e v i e w o f Sp r i gg s e t a l . [ ]. T a r g e t E n [ M e V ] A u t h o r g r r r r r r (cid:104) T (cid:105) T h ( F ) K ee p i n T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± .
006 14 . [ ] T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . a i . ± . . ± . . ± . . ± . . ± . . ± . P a ( F ) A n o u ss i s T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± .
027 14 . B r o w n T i . ± . . ± . . ± . . ± . -- . ± . ( ’ ) a i . ± . . ± . . ± . . ± . -- U ( T ) W a l d o T i . ± . . ± . . ± . . ± . . ± . - . ± . ( ’ ) a i . ± . . ± . . ± . . ± . . ± . - U ( T ) [ ] T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . a i . ± . . ± . . ± . . ± . . ± . . ± . ( F ) [ ] T i . ± . . ± . . ± . . ± . . ± . . ± . . ± .
20 0 . a i . ± . . ± . . ± . . ± . . ± . . ± .
001 14 . E a s t T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . U ( T ) [ , ] T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . a i . ± . . ± . . ± . . ± . . ± . . ± . ( F ) [ ] T i . ± . . ± . . ± . . ± . . ± . . ± . . ± .
06 0 . a i . ± . . ± . . ± . . ± . . ± . . ± . . E a s t T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . U ( F ) [ , ] T i . ± . . ± . . ± . . ± . . ± . . ± . . ± .
11 3 . a i . ± . . ± . . ± . . ± . . ± . . ± . U ( F ) [ ] T i . ± . . ± . . ± . . ± . . ± . . ± . . ± .
03 3 . a i . ± . . ± . . ± . . ± . . ± . . ± .
001 14 . [ ] T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . a i . ± . . ± . . ± . . ± . . ± . . ± . N p ( F ) [ ] T i . ± . . ± . . ± . . ± . . ± . . ± . . ± .
17 3 . a i . ± . . ± . . ± . . ± . . ± . . ± .
002 14 . [ ] T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . a i . ± . . ± . . ± . . ± . . ± . . ± . P u ( T ) W a l d o T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . ( F ) B e n e d e tt i T i . ± . . ± . . ± . . ± . . ± . - . ± . ( ’ ) a i . ± . . ± . . ± . . ± . . ± . - – C o n t i nu e d t o n e x t p ag e . . . NUCLEAR DATA SHEETS P. Dimitriou et al. T A B L E XXXV II . – C o n t i nu e d f r o m p r e v i o u s p ag e T a r g e t E n [ M e V ] A u t h o r g r r r r r r (cid:104) T (cid:105) P u ( T ) [ , ] T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . a i . ± . . ± . . ± . . ± . . ± . . ± .
002 0 . [ , ] T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . a i . ± . . ± . . ± . . ± . . ± . . ± .
001 15 . [ ] T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . a i . ± . . ± . . ± . . ± . . ± . . ± . P u ( F ) K ee p i n T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . P u ( T ) C o x T i ± . . ± . . ± . . ± . . ± . - . ± . ( ’ ) a i . ± . . ± . . ± . . ± . . ± . - ( F ) G ud k o v T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . P u ( F ) W a l d o T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± .
086 14 . E a s t T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . A m . [ ] T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . a i . ± . . ± . . ± . . ± . . ± . . ± .
001 15 . [ ] T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . a i . ± . . ± . . ± . . ± . . ± . . ± . m A m ( T ) W a l d o T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . C m ( T ) W a l d o T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . C f ( T ) W a l d o T i . ± . . ± . . ± . . ± . -- . ± . ( ’ ) a i . ± . . ± . . ± . . ± . -- C f ( S F ) C hu li c k T i . ± . . ± . . ± . . ± . -- . ± . ( ’ ) a i . ± . . ± . . ± . . ± . -- R e c o mm e nd e d - G r o up D e l a y e d N e u t r o n P a r a m e t e r s f o r A m . P a r a m e t e r s a nd s y m b o l s a s a b o v e E n A u t h o r g r r r r r r r (cid:104) T (cid:105) ( F ) C h a r l t o n T i . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . . . . NUCLEAR DATA SHEETS P. Dimitriou et al. T A B L E XXXV
III . R e c o mm e nd e d - G r o up D e l a y e d N e u t r o n P a r a m e t e r s . P a r a m e t e r s a nd s y m b o l s a s i n T a b l e XXXV II . T a r g e t E n A u t h o r g r r r r r r r r (cid:104) T (cid:105) [ M e V ] T i . . . . . . . . T h ( F ) K ee p i n ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . P a ( F ) A n o u ss i s ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . -- . ± .
19 14 . B r o w n ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . -- . ± . U ( T ) W a l d o ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . - . ± . U ( T ) [ , ] a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± .
23 0 . [ ] a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± .
23 14 . E a s t( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . U ( T ) [ ] a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± .
18 0 . [ ] a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± .
18 14 . E a s t( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . U ( F ) [ ] a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . U . [ ] a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . N p . [ ] a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . P u ( T ) W a l d o ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . - . ± . ( F ) B e n e d e tt i ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . - . ± . P u ( T ) [ , ] a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± .
22 0 . [ , ] a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . P u ( F ) K ee p i n ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . P u ( T ) C o x ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . - . ± . ( F ) G ud k o v ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . P u ( F ) W a l d o ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± .
28 14 . E a s t( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . A m . [ ] a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . m A m ( T ) W a l d o ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . - . ± . A m ( F ) C h a r l t o n ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C m ( T ) W a l d o ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . - . ± . C f ( T ) W a l d o ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . - . ± . C f ( S F ) C hu li c k ( ’ ) a i . ± . . ± . . ± . . ± . . ± . . ± . . ± . - . ± . . . . NUCLEAR DATA SHEETS P. Dimitriou et al. results has yet to be published, and then evaluated andincluded in the database.The collaborative work performed under the auspicesof the International Atomic Energy Agency (IAEA) wastimely as it will not only guide future experiments on β n emitters but will also lead to more reliable calculationsfor r -process nucleosynthesis and the new generation offission reactors. A. Microscopic experiments
The members of the CRP assessed all methods for themeasurement of half-lives, neutron-branching ratios, andneutron energy spectra, taking into account recent tech-nological developments and the requirements for futuremeasurements. The ” β -n” method using the coincidentdetection of β ’s and neutrons (and optional with subse-quent detection of γ ’s) was identified as the most reliablemethod for the measurement of neutron-branching ratios(see Sect. II A 1). If the decay scheme of a nucleus iswell-known (including absolute decay intensities and iso-meric states), also detection methods without neutronscan provide very reliable results, for example the coinci-dent ”Double γ counting method” (” γ, γ ”, Sect. II A 6).In the past years also new, pure ion-counting methodshave been developed that circumvent the necessity to de-tect neutrons, β ’s or γ ’s. These experiments have beengrouped in the ”Double ion counting” method (”ion,ion”,Sect. II A 8) and comprise techniques using various typesof traps, time-projection chambers, or even storage rings(see Sect. II C)Some of these new ion-counting techniques, namely theion-recoil detection methods, can also be used to extractthe respective neutron energy spectra. This has beenshown recently for the Beta-decay Paul trap (BPT) wherea good agreement with the measured spectrum for Iwas found, although with limited resolution due to thetrap geometry.Besides traditional techniques the neutron time-of-flight (TOF) method with fast plastic or liquid scin-tillators has shown to be the best method to measurethe neutron energy spectra. Thanks to their relativelyhigh intrinsic efficiency they can be also employed forthe measurement of rare isotopes but their limitationis the achievable resolution at higher neutron energies( > γ -ray Spectrometers (TAGS) havebeen used since many years to measure β - and γ -strengthfunctions, as well as level densities. More recently ithas been shown that they can also be used to determine P n values and delayed neutron spectra (see Sect. II C 1).This offers new exciting opportunities for the investiga-tion of important β n-emitter at RIB facilities worldwidewith complementary detection techniques.Recent experimental studies included a revisiting of theproperties of β n-emitter abundantly produced during anuclear fuel cycle in power and research reactors. Re- measurements of half-lives and neutron-branching ratiosfor nuclei on priority lists for the most important contrib-utors to the delayed neutron fraction ν d (see e.g. p. 15in Ref. [40]) have been carried out, as well as completestudies of the β -strength distribution below and abovethe neutron emission threshold and resulting β n-energyspectra. These measurements helped to refine the anal-ysis of the processes occurring in nuclear fuel during theoperation of nuclear reactors and provided data for a bet-ter theoretical analysis of the β -strength distribution.One important focus for β n-emitter studies in the fol-lowing years will be the role of competitions betweendifferent decay channels. This includes the competitionbetween one- and multi-neutron emission with the de-excitation via γ transitions from highly excited statesabove the neutron separation energy. In earlier theoret-ical models these competitions have not been included(in the case of γ competition) or only with a simplifiedcut-off picture (as in the case of competition between the1n and 2n channel). However, as has been shown in thepast years, the correct treatment of these competing de-cay channels is crucial since it can lead to systematicallywrong predictions. This can have an influence, for exam-ple, on the amount of neutrons available in late phasesof the astrophysical r process and thus lead to differentcalculated abundance distribution patterns. B. Compilation and evaluation of microscopic data
The compilation and evaluation of the half-lives andneutron-emission probabilities of all 653 presently iden-tified β n emitters between He ( Z =2) and Fr ( Z =87)has been carried out [35, 36].In total, 507 of these β n-emitter have measured β -decay half-lives and 306 have a measured P n value. How-ever, only for 32 nuclides the β -delayed two-neutron emis-sion ratio ( P n ) has been measured. The P n value is onlyknown for four nuclei so far ( Li, , B, and N), andthe result of the P n of B is only tentative.Nine standards for P n measurements with a precisionof better than 5% and four with a precision between 5-10% have been recommended by the CRP: Li, C, N, K, Ga, , Br, , Rb,
I, and , , Cs (seeTable I).In general, the precision of the measured neutron-branching ratios is much lower than for β -decay half-lives(see Fig. 61), and the neutron branching ratios of manynuclei are only available as upper (shown with 100% un-certainty) or lower limits.With the expected vast amount of new data in the nextyears, an annual re-evaluation of β n emitters is planned sothat this new data can be included in the IAEA ReferenceDatabase [43] in a timely manner. The evaluation of thelight mass region ( Z =2–28) has been published more than5 years ago [35], and work on the update has startedrecently by the Canadian nuclear data community.84evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
FIG. 61. Schematic comparison of uncertainties for P n values (top) and half-lives (bottom) for evaluated β n emitters [35, 36].Upper limits are shown with 100% uncertainty. C. Microscopic theory
Two global self-consistent microscopic models havebeen used in comparisons with the CRP evaluated mi-croscopic data ( T / , P n ): the spherical continuum pn-QRPA [151] (DF+CQRPA) based on the Fayans func-tional [149] in its new version DF3a that is suitable for(quasi-) spherical nuclei with low or zero deformation,and the spherical relativistic pnQRPA model [153] basedon the D3C* functional [154] (RHB+RQRPA) that hasbeen applied to all the nuclei across the nuclear chartincluding the deformed ones.The comparisons have focused on spherical and de-formed nuclei both in the light and heavy fission frag-ment regions, and on isotopes around the doubly closedshell nuclei Ni and
Sn which are important for theastrophysical r -process nucleosynthesis.The models perform equally well or even better thanthe widely used restricted (Q)RPA-like scheme which isbased on the microscopic-macroscopic Finite Range Liq-uid Drop Model (FRDM12+(Q)RPA+HF [148]). Theglobal self-consistent models can thus be recommended for planning RIB experiments and for predictions in massregions where measurements are not possible and whichare important for astrophysical modeling.Both models, DF+CQRPA and RHB+QRPA, treatthe contributions of the first-forbidden (FF) and the al-lowed Gamow-Teller (GT) transitions fully microscopi-cally and on equal footing. However, the comparison withthe evaluated ( T / , P n ) data shows that the β -decay ob-servables are extremely sensitive to the competition be-tween the GT and FF strengths, the isoscalar pn-pairing-like NN-interaction, and the ground-state spin inversioncaused by the neutron-proton tensor interaction whichmay cause a stabilization effect . This leads to a slowingdown of the rate at which the half-life decreases with in-creasing mass number, as well as other irregularities inthe P n values.These findings underscore the need to further improvethe nuclear energy-density functional, in particular thepairing and tensor parts of the functional. The recentlyproposed hybrid density functional [292] that uses theSkyrme functional with a pairing part depending on thegradient of density, as in the Fayans functional [149], hasthe potential to describe both the odd-even staggering ef-85evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al. fects in the Q β values and charge radii [293], and the two-neutron emission probabilities [177, 183]. Also promis-ing are the newly developed “beyond the QRPA” self-consistent models that take into account the impact of thephonon-phonon [164, 165] or quasiparticle-phonon [166–168, 294] couplings on the β -decay properties. D. Summation and time-dependent calculations
The evaluated ( T / , P n ) values were used in summa-tion and time-dependent calculations of total delayedneutron yields ν d , DN activity, and DN spectra in combi-nation with the cumulative fission yields from the JEFF-3.1.1 library. Overall, the CRP microscopic data lead toenhanced ν d values, partly due to the increased P n valueof I which is the main contributor to nearly all the fis-sion systems studied. The results of the present summa-tion calculations, nevertheless, are in better agreementwith the ν d values recommended by WPEC-SG6 [14]compared to those of Wilson [187] which were based onprevious compilations of P n data. The best agreementwith recommended ν d values is obtained for thermal fis-sion of U and
Pu, for which we have the most re-liable fission yield data, while for
U fast fission thereis significant improvement. In the case of fast fission of
U and
Pu, as well as fission of
Pu, however, therecommended values are overestimated.Time-dependent kinetic parameters were calculatedstarting from the microscopic recommended CRP data( T / , P n ) and the JEFF-3.1.1 independent fission yields,taking into account correlations in the decay path. Theestimated group abundances are affected by larger un-certainties than the measured ones indicating that amore comprehensive approach to treating correlations isneeded that would include contributions from fission yielddata. Both summation and time-dependent calculationsprovide clear evidence of the energy dependence of thetotal DN yields for the fission of U and
Pu. Theseresults confirm the need for a more detailed investigationof the energy dependence of fission yields and a subse-quent updating of the fission yield libraries.Though the new microscopic CRP ( T / , P n ) databaseis significantly improved with respect to previous datedcompilations, the impact on integral DN properties alsodepends strongly on the fission yield library that wasused. In addition, the uncertainties in the integral quanti-ties do not take into account correlations affecting the fis-sion yield data, therefore they could be underestimated.We strongly recommend, as a next step, that the eval-uated fission yield libraries are updated with due con-sideration of correlation effects and the dependence onincident energy. E. Integral experiments and reactor calculations
The impact of the new evaluated microscopic dataon integral experiments and specific reactor designs hasbeen assessed. Integral calculations were performed us-ing different evaluated libraries and the CRP ( T / , P n )data. The results show that β eff values obtained fromthe combination of JEFF-3.1.1 fission yields with theCRP data and supplementary ENDF/B-VIII.0 decaydata give slightly increased β eff values with respectto the other libraries for the benchmark experimentsPOPSY, TOPSY, JEZEBEL, SKI-DOO, FLATTOP-23,BIG TEN, SNEAK-7A,SNEAK-7B and IPEN.Similar results were obtained for three different re-actor designs, a pressurized water reactor (PWR), thesodium cooled ASTRID reactor and the lead-bismuthcooled MYRRHA reactor. The combination of the CRPdata with JEFF-3.1.1 fission yields leads to β eff valuesthat deviate from the reference values by 1-2% for PWRand MYRRHA and 11% for ASTRID.These results depend strongly on the fission yield li-brary that was used, therefore, as has been stressedabove, further studies using updated fission yield librarieswould be required before a definitive conclusion is drawn. F. Macroscopic measurements and systematics
The total delayed neutron yields have been measuredin the energy range from 0.3 to 5 MeV for nuclides ofimportance to reactor technology and applications. Incontrast to the results obtained from β eff methods, thesemeasurements show an energy dependence that does notagree with the recommended data currently available inthe evaluated libraries.The time-dependent integral DN energy spectra havebeen measured for thermal neutron-induced fission of U. For the first time, the consistency of macroscopicDN spectra with the spectra obtained from the summa-tion calculations over microscopic data ( T / , P n ) for in-dividual precursors has been demonstrated.The energy dependence of DN temporary group pa-rameters ( a i , T i ) have been studied in the energy rangefrom thermal to 18 MeV. A procedure for averaging DNparameters obtained in different experimental runs hasbeen developed. DN group parameters have been deter-mined experimentally in an extended time of DN count-ing compared to previous measurements by Keepin [13].The correlation and covariance matrices for the DN tem-porary group parameters have been extracted.These studies have revealed the reasons behind thelarge discrepancies observed in the temporary parametersin the energy range 14-18 MeV. They have also led to thedevelopment of new systematics for the DN temporaryparameters which have enhanced predictive power.86evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al.
G. New recommendations of group constants
Finally, new recommendations have been made for theDN temporary group parameters ( a i , T i ) in 6- and 8-group models based on the evaluation of the new ex-perimental macroscopic data. As the validation of thesegroup models was beyond the scope of this CRP, it re-mains for the user community to use these new recom-mended data in verification and validation studies. Thenew recommended ( a i , T i ) data are available in this re-port and from the online CRP database [43]. ACKNOWLEDGMENTS
This work has been performed in the framework ofa Coordinated Research Project of the InternationalAtomic Energy Agency (IAEA) on ”Development of aReference Database for β -delayed neutron emission data”(F41030).I.D.’s work was partly funded by the Natural Sci-ences and Engineering Research Council (NSERC) andthe Natural Research Council (NRC) Canada. B. S.’swork was partly funded by the Nuclear Data Section ofthe IAEA. I.N.B. was supported by the Russian ScienceFoundation under Grant No. 16-12-10161.K.R. was partially supported by the US DOE Officeof Science, Nuclear Physics) under the contract numberDE-AC05-00OR22725 with UT Battelle, LLC. Work atBrookhaven National Laboratory was sponsored by theOffice of Nuclear Physics, Office of Science of the U.S.Department of Energy under Contract No. DE-AC02-98CH10886 with Brookhaven Science Associates, LLC.Work at Lawrence Livermore National Laboratory wasperformed under the auspices of the U.S. Department ofEnergy under Contract DE-AC52-07NA27344.Work at IFIC (A.A., J.L.T.) was supported by theSpanish Ministerio de Econom´ıa y Competitividad un-der Grants No. FPA2011-24553, No. FPA2014-52823-C2-1-P, FPA2017-83946-C2-1-P, and the program SeveroOchoa (SEV-2014-0398).Work at CIEMAT was supported by the Spanish na-tional company for radioactive waste management EN-RESA, through the CIEMAT-ENRESA agreements on“Transmutaci´on de radionucleidos de vida larga como so-porte a la gesti´on de residuos radioactivos de alta ac-tividad” and by the Spanish Ministerio de Econom´ıa yCompetitividad under Grants No. FPA2014-53290-C2-1-P and FPA2016-76765-P.Work at SUBATECH was supported by the CNRSchallenge NEEDS and the associated NACRE project,and by the CNRS/in2p3 Master Project OPALE. 87evelopment of a Reference Database . . . NUCLEAR DATA SHEETS P. Dimitriou et al. [1] R.B. Roberts, R.C. Meyer, and P. Wang, “Further ob-servations on the splitting of Uranium and Thorium,”
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