Energy dependence of the prompt γ -ray emission from the (d,p) -induced fission of 234 U ∗ and 240 Pu ∗
S. J. Rose, F. Zeiser, J. N. Wilson, A. Oberstedt, S. Oberstedt, S. Siem, G. M. Tveten, L. A. Bernstein, D. L. Bleuel, J. A. Brown, L. Crespo Campo, F. Giacoppo, A. Görgen, M. Guttormsen, K. Hadyńska, A. Hafreager, T. W. Hagen, M. Klintefjord, T. A. Laplace, A. C. Larsen, T. Renstrøm, E. Sahin, C. Schmitt, T. G. Tornyi, M. Wiedeking
EEnergy dependence of the prompt γ -ray emission from the (d,p)-induced fission of U* and
Pu*
S.J. Rose, ∗ F. Zeiser, † J.N. Wilson, A. Oberstedt, S. Oberstedt, S. Siem, G.M. Tveten, L.A. Bernstein,
5, 6
D.L. Bleuel, J.A. Brown, L. Crespo Campo, F. Giacoppo, ‡ A. G¨orgen, M. Guttormsen, K. Hady´nska, A. Hafreager, T.W. Hagen, M. Klintefjord, T.A. Laplace,
6, 7
A.C. Larsen, T. Renstrøm, E. Sahin, C. Schmitt, T.G. Tornyi, and M. Wiedeking Department of Physics, University of Oslo, 0316 Oslo, Norway Institut de Physique Nucl´eaire d’Orsay, CNRS/ Univ. Paris-Sud,Universit´e Paris Saclay, 91406 Orsay Cedex, France Extreme Light Infrastructure - Nuclear Physics (ELI-NP) / Horia Hulubei National Institutefor Physics and Nuclear Engineering (IFIN-HH), 077125 Bucharest-Magurele, Romania European Commission, Joint Research Centre, Directorate for Nuclear Safety and Security,Unit G.2 Standards for Nuclear Safety, Security and Safeguards, 2440 Geel, Belgium Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA University of California - Berkeley Dept. of Nuclear Engineering, Berkeley CA 94720, USA Lawrence Livermore National Laboratory, Livermore, CA 94551, USA Grand Acc´el´erateur National d’Ions Lourd, Bd Henri Becquerel, BP 55027 - 14076 CAEN Cedex 05, France iThemba LABS, P.O. Box 722, 7129 Somerset West, South Africa (Dated: October 20, 2018)Prompt fission γ -rays are responsible for approximately 5% of the total energy released in fission,and therefore important to understand when modelling nuclear reactors. In this work we presentprompt γ -ray emission characteristics in fission, for the first time as a function of the nuclear excita-tion energy of the fissioning system. Emitted γ -ray spectra were measured, and γ -ray multiplicitiesand average and total γ energies per fission were determined for the U(d,pf) reaction for excita-tion energies between 4.8 and 10 MeV, and for the
Pu(d,pf) reaction between 4.5 and 9 MeV.The spectral characteristics show no significant change as a function of excitation energy above thefission barrier, despite the fact that an extra ∼ γ -decay. The measured results are compared to model calculations made for prompt γ -ray emission with the fission model code GEF. Further comparison with previously obtained re-sults from thermal neutron induced fission is made to characterize possible differences arising fromusing the surrogate (d,p) reaction. PACS numbers:
I. INTRODUCTION
Nuclear fission was discovered some 70 years ago [1–3],but still there remain some intriguing mysteries aboutthis complex process. One of the least measured parts ofthe energy that is released in fission is the contributionthat is carried away via prompt γ -ray emission. Thisaccounts for roughly 8 MeV [4, 5], or around 5% of thetotal energy released in fission. In addition, prompt en-ergy is dissipated via the Coulomb repulsion of the frag-ments, and the emission of prompt neutrons. Promptfission γ -rays (PFG) are emitted, typically within a fewnanoseconds of scission of the fragments; about 70% ofthe prompt PFGs are emitted within 60 ps [6], and about95% within 3 ns [7]. PFGs are one of the least understoodparts of the fission process [8].The investigation of PFG emission addresses questions ∗ Corresponding author: [email protected] † Corresponding author: [email protected] ‡ Current affiliation: a) Helmholtz Institute Mainz, 55099 Mainz,Germany b) GSI Helmholtzzentrum f¨ur Schwerionenforschung,64291 Darmstadt, Germany in nuclear structure and reaction physics. One ques-tion deals with the de-excitation of nuclei through theemission of neutrons and γ -rays. The theoretical de-scription of the de-excitation of neutron-rich isotopes, asbeing produced in neutron-induced fission, shows signifi-cant deficits in describing the neutron and γ -ray spectralshape [8]. To some extent this deficiency seems to be re-lated to a limited understanding of the competing processof prompt neutron and γ emission. Prompt fission γ -rayspectral (PFGS) data, measured as a function of excita-tion energy of the compound nucleus may provide impor-tant information to benchmark different models, allowingeventually arrival at a consistent description of promptfission neutron and γ -ray emission. Furthermore, PFGsare certainly among the most sensitive observables forstudying angular momentum generation in fission [8, 9].Understanding the PFG emission is not only useful forcomplete modelling of the fission process, but it also hassome important practical applications for nuclear reac-tors. In recent years, requests for more accurate PFGSdata have motivated a series of measurements to obtainnew precise values of the γ -ray multiplicities and meanphoton energy release per fission in the thermal-neutroninduced fission of U [10, 11] and
Pu [11, 12]. With a r X i v : . [ nu c l - e x ] J u l the development of advanced Generation-IV nuclear re-actors, the need of new PFGS data becomes important.Since four out of six contemplated Generation-IV re-actors require a fast-neutron spectrum, a wider rangeof incident neutron energies has to be considered [13].Modelling of the geometrical distribution of γ -heating,in and around the reactor core, shows local deviationsup to 28% as compared to measured heat distributions,whereas accuracy within 7.5% is mandatory [14]. Thesedeviations remain mainly, despite experiment campaignsin the 1970s [4, 15–17], due to the uncertainties on the ex-isting PFGS data [10, 18, 19]. For Pu*, this work alsoresponds to the high-priority request published throughthe OECD/NEA [14].In this paper we report about the first measurements ofPFG emission from
U* in the
U(d,pf) reaction, and
Pu* in the
Pu(d,pf) reaction. Both target nucleirepresent the fissile key nuclei for the thorium/uraniumand uranium/plutonium fuel cycles, respectively. The(d,pf) reaction serves hereby as a surrogate for the neu-tron induced fission [20]. Charged-particle induced reac-tions allow measurements of fission observables for iso-topes not easily accessible to neutron beam experiments,or for excitation energies below the neutron binding en-ergy. They also facilitate the study of PFG characteris-tics as a function of compound nucleus excitation energy.We study the dependence of PFG characteristics on com-pound nucleus excitation energy, and possible differencesbetween surrogate and neutron-induced fission reactions.
II. EXPERIMENTAL DETAILS
Two experiments, denoted by (A) and (B), were car-ried out at the Oslo Cyclotron Laboratory (OCL) of theUniversity of Oslo, using deuteron beams, delivered bya MC-35 Scanditronix cyclotron. The γ -detector arrayCACTUS [21] together with the SiRi charged particledetectors [22] and the NIFF detector [23] were used todetect triple coincident events of a proton, one of the twofission fragments (FF) and γ -rays.Experiment (A) utilized a 12.5 MeV beam incident ona U target, and experiment (B) had a 12 MeV beam ona
Pu target (detailed target specifications are listed inTable I). The targets were cleaned from decay productsand other chemical impurities with an anion-exchangeresin column procedure [24], and then electroplated on abacking made of Be.For these particular experiments, the SiRi detectorswere mounted in backward direction, and the NIFF de-tectors in forward direction, relative to the beam direc-tion (see Fig. 1). This setup was chosen for severalreasons: Due to the thick beryllium backing, the tar-gets had to face NIFF, to enable detection of any fissionevents, thereby also avoiding FF in the SiRi detector.However, the light, outgoing particles could easily pene-trate the beryllium, and be detected in SiRi. Backwarddirection of SiRi also reduces the intensity of the elas-
TABLE I. Target and beam characteristics as used in thiswork. Fission barrier heights are taken from Ref. [25]Target
U (A)
Pu (B)Chemical composition metallic metallicActive diameter 1 cm 1 cm Be backing (mg/cm ) 2.3 1.8Total area density (mg/cm ) 0.2 0.4Reaction (d,pf) (d,pf)Beam energy (MeV) 12.5 12Inner fission barrier, B F , a (MeV) 4.80 6.05Outer fission barrier, B F , b (MeV) 5.50 5.15 tic peak, and minimizes the exposure to protons fromdeuteron breakup in the target. SiRi was covered by a21 µ m thick aluminum foil, to attenuate δ -electrons inthe telescopes.SiRi consists of 64 ∆E (front) and 8 E (back) silicondetectors with thicknesses of 130 µ m and 1550 µ m, re-spectively. The detectors cover eight angles from θ (cid:39) ◦ to 140 ◦ relative to the beam axis, in a lampshadegeometry facing the target at a distance of 5 cm at an an-gle of 133 ◦ . The total solid angle coverage is about 9% of4 π . In experiment (A) twenty-five, and in experiment (B)twenty-six, 12.7 cm × (cid:48)(cid:48) × (cid:48)(cid:48) ) NaI(Tl) crystalswere mounted on the spherical CACTUS frame, 22 cmaway from the target. At a γ -ray energy of 1.33 MeV, thecrystals detect γ -rays with a total efficiency of 13.6(1)%(A), and 14.2(1)% (B), respectively. In order to reducethe amount of Compton scattering, the detectors werecollimated with lead cones. NIFF, consisting of four Par-allel Plate Avalanche Counters (PPAC), covering 41% of2 π , were used for tagging of fission events. For this, itis sufficient to detect one of the two fission fragments,which are emitted back-to-back. The PPACs are placedat an angle of 45 ◦ with respect to the beam axis, at a dis-tance of about 5 cm from the centre of the target. Takinginto account angular anisotropy effects in the center-of-mass system, Ref. [26] found a total efficiency of about48%. The particle and fission detectors were mounted inthe reaction chamber, surrounded by the CACTUS ar-ray (Fig. 1). The experiments were running for one weekeach, with a typical beam current of 1 nA.The experimental setup enables particle-FF- γ coinci-dences that, together with energy and time information,are sorted event-by-event. In the present work, we fo-cused on the U(d,pf) and the
Pu(d,pf) reactions.The detection of a charged particle in SiRi was the eventtrigger. In a timing interval of ∼
20 ns we require a γ -signal in CACTUS and a FF in NIFF.From kinematics the measured energy of the outgo-ing, charged particle is converted into initial excitationenergy, E x , of the fissioning system. In our cases, wemeasure the deposited energy of the proton in the parti-cle telescope, thereby selecting U* and
Pu* as thefissioning system, for experiments (A) and (B), respec-tively. The excitation energy was reconstructed event-
FIG. 1. (Color online) Schematic view of the experimentalset-up for experiment (A), showing the SiRi (∆E+E) tele-scope, and the NIFF (PPAC) detectors, inside the reactionchamber, surrounded by the CACTUS NaI array. SiRi mea-sures the energy of the outgoing charged-particles; NIFF de-tects fission fragments (FF), and CACTUS detects γ -rays allin coincidence, within a time interval of 20 ns. The U tar-get (0.2 mg/cm , green), on the Be backing (2.3 mg/cm ,orange) was facing NIFF, and SiRi was in the backward di-rection relative to the beam direction (dotted, purple arrow).The setup for the Pu experiment was identical, except forCACTUS having 26 crystals instead of 25. by-event from the detected proton energy and emissionangle, and accounting for energy losses in the target andbacking. For each energy bin in E x , a correction forthe neutron contribution to the γ -ray spectrum is per-formed, which is detailed in the next section. Finally,the raw γ -spectra are corrected for the detector responseto produce a set of unfolded PFGS. The applied unfold-ing process, which has the advantage that the original,statistical fluctuations are preserved, is fully described in[27]. NaI response functions are based on in-beam γ -linesfrom excited states in , Fe, Si, O, and C, whichwere re-measured in 2012 [28].
A. Correction for neutron contribution
In the fission process, both neutrons and γ -rays areemitted. Neutrons can interact with the NaI crystals ofCACTUS, depositing energy mostly in the form of γ -rays from (n,n (cid:48) γ ) reactions. Unfortunately, the timinggate (20 ns) of the current set-up (Fig. 1) only allows fordiscrimination between γ -rays and neutrons via time-of-flight (TOF) for the slowest neutrons, i.e. with energieslower than 600 keV. However, the majority of promptneutrons emitted in fission have higher energy than this.To obtain PFGS, a correction for the neutron componentneeds to be made, with subtraction of counts arising fromenergy deposition by neutrons. TABLE II. Parameters to scale the excitation energy depen-dence of the average total neutron multiplicity relative to theneutron separation energy S n extracted from Ref. [31] ( U*)and Ref. [32] (
Pu*). U* Pu*a (n/MeV) 0.1 0.14b (¯ ν @ thermal fission) 2.5 2.9 S n (MeV) 6.85 6.53 Our neutron correction method relies on using a neu-tron response spectrum of a NaI detector, which is mostrepresentative of that for fission neutrons. Normalizingthis to the known average neutron multiplicity emitted infission for a particular compound nucleus excitation en-ergy allows estimation of the neutron component in thetotal measured PFGS at this energy. This component isthen subtracted. In this work we used a spectrum [29] for2.3 MeV neutrons, which is close to the average fissionneutron energy.The response of 7.6 cm × (cid:48)(cid:48) × (cid:48)(cid:48) ) NaI detec-tors to incident neutrons at energies between 0.4 and 10MeV has been measured by H¨ausser et al. [29], using aTOF discrimination with quasi-monoenergetic neutronsproduced in the Li(p,n) and
Au(p,n) reactions. Theyfind that the neutron response is dominated by (n,n (cid:48) γ )reactions. For the energies most prominent from fissionneutrons, 1-2.5 MeV, most counts in the NaI detectorsare observed between 0.4 and 1 MeV. For 2.3 MeV neu-trons, they report 0.13(5) triggers per incident neutron.Since the CACTUS detectors are longer (12.5 cm), wescale the number of triggers to 0.21(8) triggers per in-cident neutron. We assume that the intrinsic detectionefficiency, (cid:15) int , for γ -rays from fission is the same as thosecreated in the detector by (n,n (cid:48) γ ) reactions. The γ -raymultiplicity, ¯ M , for neutron contribution correction pur-poses is taken as 6.31 for U* [17] and 7.15 for
Pu*[30].The relative contribution, f , of neutrons to the mea-sured data N tot ( E x , E γ ) for each excitation energy E x and γ -ray energy bin E γ can be estimated by the detec-tion efficiencies. Taking into account the ratio of neutronand γ -ray multiplicities we find f = (cid:15) int , n ¯ ν(cid:15) int , n ¯ ν + ¯ M . (1)The neutron multiplicity ¯ ν is known to vary approxi-mately linearly as a function of the incident neutron en-ergy E n [31–33]. Taking into account the neutron separa-tion energy S n , the same dependence is assumed for thecompound nucleus excitation energy E x with the param-eters given in Table II, such that ¯ ν ( E x ) = a ( E x − S n ) + b .The total contribution to the data caused by neutrons isestimated as a fraction of counts, f ( E x ), that is weightedas a function of E γ by H¨aussers neutron spectrum H ( E γ ),i.e. N n ( E x , E γ ) = N tot ( E x ) f ( E x ) H ( E γ ) , (2) TABLE III. Values used for calculating the neutrons in theCACTUS detectors. The average neutron energies were cal-culated from ENDF/B VII.1 [34]. Neutron multiplicities ¯ ν are taken from Ref. [31, 32] and γ -ray multiplicities ¯ M , fromRef. [17] ( U*) and Ref. [30] (
Pu*).A (
U*) B (
Pu*)Average neutron energy (MeV) 2.0 2.1Intrinsic neutron efficiency(triggers/neutron) 0.21(8) 0.21(8)Neutron multiplicities(@ thermal fission) 2.5 2.9 γ -ray multiplicities 6.31(30) 7.15(9)Relative contribution(@ thermal fission) 0.0768 0.078 where N tot ( E x ) is the projection of the γ -matrix onto E x N tot ( E x ) = (cid:88) E γ N tot ( E x , E γ ) . (3) N tot ( E x , E γ ) is the matrix element in the γ -matrix. H ( E γ ) is normalized so that (cid:80) E γ H ( E γ ) = 1 . The γ -ray spectrum N γ ( E x , E γ ) is obtained by subtracting theneutron contribution N n ( E x , E γ ) from the measured data N tot ( E x , E γ ) N γ ( E x , E γ ) = N tot ( E x , E γ ) − N n ( E x , E γ ) . (4)The results of the subtraction procedure can be seengraphically in Fig. 2, where the raw spectrum, neutroncontribution and corrected spectrum are shown. Sinceinelastic scattering is the main energy deposition mech-anism for neutrons, which occurs mostly on low-lyingstates in sodium and iodine nuclei, the neutron contri-bution is largest in the low energy part of the spectrum.However, overall, the correction for neutron contributionin our experiments remains small (see Table III). B. Extrapolation of spectra towards zero energy
Detectors used in experiments that attempt to mea-sure PFGS will always have an energy threshold to pre-vent rapid triggering on noise. Below this threshold γ -raydetection is impossible, so the lowest energy γ -rays emit-ted in fission will not be detected. As a consequence,this will introduce a systematic uncertainty in the de-duction of average spectral quantities: Measured multi-plicities ¯ M and total γ -energy E tot will thus be lower,and measured average γ -ray energy E av released per fis-sion will be higher, than their actual values. In fact, suchsystematic uncertainties from threshold effects may ex-plain discrepancies between previous PFG experimentalresults, [10, 35]. To account for the undetected γ -raysbelow threshold, it is necessary to make an extrapola-tion towards zero energy, such as e.g. that performed in FIG. 2. (Color online) The total (summed over all E x ) rawPFGS detected in the U(d,pf) reaction (black) and thecalculated spectral contribution due to interactions of promptfission neutrons in the NaI detector (green). The corrected γ -spectrum is also shown (pink). Ref. [36]. In our case the detection threshold was ratherhigh, at 450 keV. As the shape of the γ ray spectrumis not known for the low γ -ray energies, we chose a con-stant value for the bins below threshold. A reasonableextrapolation of each spectrum was made by averagingover the first three γ -ray bins above the threshold. Theuncertainty was estimated by the minimum and maxi-mum values in these bins, including their uncertainties.This results in an average value of about 5 . ± U*), below threshold. Byassuming a non-zero value for this energy bin, the extrap-olation reduces the uncertainty, but it does not eliminateit entirely. In our case it is still the dominant source ofuncertainty on the absolute values of the average spec-tral quantities deduced. Since we compare our data withthermal neutron induced fission experiments, we chosethe same cutoff of the PFGS as Ref. [16], of E γ =140keV. III. PREDICTIONS WITH THE GEF CODE
We compare our data to predictions from the semi-empirical GEneral Fission model (GEF) [37]. GEF isbased on the observation of a number of regularities in fis-sion observables, revealed by experimental studies, com-bined with general laws of statistical and quantum me-chanics. It provides a general description of essentiallyall fission observables (fission-fragment yields and kineticenergies, prompt and delayed neutrons and γ -rays, andisomeric ratios) in a consistent way while preserving thecorrelations between all of them. GEF has shown to beable to explain in an unprecendented good manner fis-sion fragment and neutron properties over a wide range,running from spontaneous fission to induced fission upto an excitation energy of about 100 MeV for Z = 80to Z = 112 [37]. Modelling of γ -rays in fission has beenimplemented most recently. In contrast to other existingcodes in the field, GEF provides also reliable predictionsfor nuclei for which no experimental data exist. This isparticularly important in our case, since no experimentaldata on the fragment properties exist for the majority ofthe excitation energies we are investigating.Calculations were performed for fission of both U*and
Pu*, applying the same cutoff of the PFGS as forthe experimental data, of 140 keV, as described in sec-tion II B. The total angular momentum J = I + L trans is the sum of the target nucleus ground state spin I andthe angular momentum L trans transferred in the (d,p)reaction. The distribution in the GEF v.2016/1.1 calcu-lations is given by ρ ( J ) ∝ (2 J + 1) exp( − J ( J + 1) /J ) , (5)where we used the root mean square (rms) of the totalangular momentum J rms and the excitation energy todescribe the fissioning system as input. The maximumvalue for J rms of 12 was obtained from J rms = √ T I / (cid:126) ,[38] where the nuclear temperature was chosen to be T ≈ .
45 MeV in line with other actinide nuclei [39, 40].The rigid body of moment of inertia I is given by m A ( r A / ) (1 + 0 . β ) ≈ (cid:126) c ) /M eV , where weused the isotope mass m A , the mass number A , thequadrupole deformation β from Ref. [25], and radiusparameter r (cid:46) .
3. The results are compared to anintermediate value of J rms = 8, and to the lower limit, J rms = 0, where the latter facilitates the comparison toneutron induced reactions, which transfer little angularmomentum. Additionally we performed calculations fora energy dependent J rms , which was adopted from thesystematics of Ref. [41] J ( E x ) = 2 × . A / (cid:112) a ( E x − E )2 a , (6)where the level density parameter a and the energy back-shift E are obtained from a fit to experimental data [41]. IV. EXPERIMENTAL RESULTSA. The
U* case
Fig. 3 shows a three-dimensional overview of the dataset where, for a given compound nucleus excitation en-ergy, the corresponding raw detected PFGS (prior tounfolding the response function) is displayed with the J rms can be expressed in terms of the spin cut-off parameter σ by J rms = √ σ FIG. 3. (Color online) Matrix of the fission and proton gatedraw γ -data from the U(d,pf) reaction (after subtractionof the contribution from neutrons). The x-axis gives the de-duced compound nucleus excitation energy E x . The y-axisgives the detected γ -ray energy, and the z-axis gives the num-ber of counts recorded during the experiment (not efficiencycorrected). The bin width is 64 keV for E x and E γ . neutron contribution subtracted. The excitation energyrange, over which the data are collected, can be seenmore closely in Fig. 4., which histograms the double co-incidences of protons and fission fragments (d,pf) andtriple coincidences of protons, fission fragments and γ -rays (d,pf γ ) as a function of E x . In the case of U*,only a very few sub-threshold fission events occur belowthe inner fission barrier [25] at E x = 4.8 MeV, which is 2MeV below the neutron separation energy at 6.85 MeV[42]. The U(d,pf) reaction at 12.5 MeV incident en-ergy populates compound nuclear excitation energies upto a maximum of 10 MeV in this case.The E x range is divided into 8 bins, each with a widthof 650 keV to obtain a sufficient statistics PFGS for eachbin. Each spectrum is unfolded for the CACTUS re-sponse, and normalized to the number of fission eventsdetected in that excitation energy bin. The set of eightnormalized spectra is overlaid in Fig. 5, and they exhibitsimilar spectral shapes.The average spectral quantities after extrapolation tozero energy are then deduced and plotted as a functionof the excitation energy. These results are plotted inFig. 6 with their corresponding statistical error bars andcompared with calculations from the GEF code. Thewider band denoted by the dash-dotted lines indicatesthe sum of the statistical uncertainties on each data pointplus the systematic uncertainty on the absolute values [MeV] x Excitation energy E C oun t s / M e V U(d,pf) ) g U(d,pf n S F,a B F,b B FIG. 4. (Color online) The total number of
U(d,pf)and
U(d,pf γ ) events recorded during the experiment his-togrammed as a function of the deduced compound nuclearexcitation energy of U* for each event. The inner and outerfission barrier, B F , a at 4.80 MeV and B F , b at 5.50 MeV, andthe neutron separation energy, S n , at 6.85 MeV are shown.The dotted lines indicates the minimum and maximum E x ofthe analysed area. The lower limit on E x is the inner fissionbarrier. [MeV] g E0 1 2 3 4 5 6 7 8 9 P ho t on s / ( F i ss i on M e V ) -3 -2 -1 = 4.8 - 5.45 MeV x E = 5.45 - 6.1 MeV x E = 6.1 - 6.75 MeV x E = 6.75 - 7.4 MeV x E = 7.4 - 8.05 MeV x E = 8.05 - 8.7 MeV x E = 8.7 - 9.35 MeV x E = 9.35 - 10 MeV x E FIG. 5. (Color online) Overlay of the eight
U(d,pf) PFGSfor different excitation energy bins in compound nucleus exci-tation energy E x . The spectra are normalized to the numberof photons per fission and per MeV to provide a comparisonof the spectral shapes. The extrapolation from the detectorthreshold at 450 keV towards zero energy is explained in thetext. due to the presence of the detection threshold. B. The
Pu* case
The same analysis was performed for the
Pu(d,pf)reaction. The (d,pf) and the (d,pf γ ) reactions are his-togrammed as functions excitation energy (Fig. 7). Inthe Pu* case, there appears to be a significant amount - e n e r g y [ M e V ] g To t a l - e n e r g y [ M e V ] g A ve r a g e Present exp.=0 rms
GEF J =8 rms
GEF J =12 rms
GEF J ) x (E rms GEF JPleasonton (1973) [MeV] x Excitation energy E5 6 7 8 9 10 M u l t i p li c i t y FIG. 6. (Color online) Energy dependence of the
U(d,pf)average PFG spectral quantities compared with calculationsfrom the GEF code for different J rms of the U* nucleus. Inaddition, results from Pleasonton [17] are shown. Multiplicity,average γ -ray energy, and total γ -ray energy, as function of ex-citation energy of U* are shown. The error bars representthe statistical uncertainty of the measurement. The dash-dotted lines represent the total uncertainty, which is the sumof the systematic uncertainty on the absolute values due to thedetector threshold, and the extrapolation towards zero energyplus the statistical uncertainty. Vertical lines mark the innerand outer fission barriers ( E x = 4.8 MeV and E x = 5.40 MeV)and the neutron separation energy ( E x = 6.85 MeV), respec-tively. of sub-barrier fission, which is in accordance with obser-vations in Refs. [43, 44]. This can be explained in thedouble-humped fission barrier picture; by the resonantpopulation of states in the second potential minimum ofthe Pu* nucleus and a tunnelling through the outerfission barrier.The overlay of the unfolded PFGS for the
Pu(d,pf)reaction is shown in Fig. 8. The spectral shapes are allobserved to be similar. However, the PFGS for the twolowest compound nucleus excitation energy bins startingat 4.65 MeV and 5.45 MeV appear to be significantlylower than the others. This effect also manifests itself inthe average photon multiplicity ¯ M and total energy E tot release at this energy (see Fig. 9). We note that this is [MeV] x Excitation energy E C oun t s / M e V
10 Pu(d,pf) ) γ Pu(d,pf n S F,a B F,b B FIG. 7. (Color online) The total number of
Pu(d,pf)and
Pu(d,pf γ ) events recorded during the experiment his-togrammed as a function of the Pu* deduced excitationenergy event-by-event. The inner and outer fission barrier, B F , a at 6.05 MeV and B F , b at 5.15 MeV, and the neutronseparation energy, S n , at 6.53 MeV are shown. The dottedlines indicates the minimum and maximum E x of the analysedarea. The lower limit of E x is at 4.8 MeV, which is more than1 MeV below the fission barrier due to sub barrier fission. [MeV] g E P ho t on s / ( F i ss i on M e V ) -3 -2 -1 = 4.5 - 5.11 MeV x E = 5.11 - 5.73 MeV x E = 5.73 - 6.34 MeV x E = 6.34 - 6.96 MeV x E = 6.96 - 7.57 MeV x E = 7.57 - 8.19 MeV x E = 8.19 - 8.8 MeV x E FIG. 8. (Color online) Overlay of the six
Pu(d,pf) unfoldedPFG gamma spectra for different excitation energy bins incompound nucleus excitation energy E x . The spectra are nor-malized to the number of photons per fission and per MeV toprovide a comparison of the spectral shapes. The extrapola-tion between 140 keV energy and the detector threshold at450 keV is explained in the text. the region below the fission barrier and, hence, originatesfrom sub-barrier fission. Otherwise, the trends for thespectral characteristics seem to have no significant trendand are fairly constant, i.e. independent of excitationenergy and thus consistent with the predictions of theGEF code.Finally, we compare the measured PFGS at excitationenergy of 6.5 MeV, which corresponds to the thermal - e n e r g y [ M e V ] g To t a l Present exp.=0 rms
GEF J =8 rms
GEF J =12 rms
GEF J ) x (E rms GEF JVerbinski et al. (1973)Pleasanton (1973) - e n e r g y [ M e V ] g A ve r a g e [MeV] x Excitation energy E4.5 5 5.5 6 6.5 7 7.5 8 8.5 M u l t i p li c i t y FIG. 9. (Color online) Energy dependence of the
Pu(d,pf)PFG average spectral quantities from the GEF code for dif-ferent J rms of the Pu* nucleus. The thermal neutron dataof Pleasonton (1973) [17] and Verbinski et al. (1973) [16] areshift slightly around S n for better visibility. Multiplicity, aver-age γ -ray energy, and total γ -ray energy, as function of excita-tion energy of Pu* are shown. The error bars represent thestatistical uncertainty of the measurement. The dash-dottedlines represent the systematic uncertainty on the absolute val-ues due to the detector threshold and the necessary extrapo-lation to zero energy. Vertical lines mark the inner and outerfission barriers ( E x = 6.05 MeV and E x = 5.15 MeV) and theneutron separation energy ( E x = 6.5 MeV), respectively. neutron induced fission reaction for Pu, with the mea-sured PFGS of Verbinski et al. [16] for thermal neutroninduced fission. Fig. 10 shows this comparison along witha spectrum from the GEF code. An excess of counts isobserved between 2 and 4 MeV for our surrogate PFGSmeasured in the
Pu(d,pf) reaction as compared to theneutron induced reaction.
V. DISCUSSION
In this study, both experiments reveal an approxi-mately constant behaviour of average γ -ray energy E av ,¯ M , and E tot , as a function of E x of the fissioning system; [MeV] g E P ho t on s / ( F i ss i on M e V ) -3 -2 -1 = 6.34 - 6.96 MeV x EVerbinski = 6.53 MeV x GEF at E
FIG. 10. (Color online) A comparison of the
Pu(d,pf)PFGS measured at E x ∼ S n (red), the PFGS for thermalneutron induced fission Pu(n th ,f) from Verbinski et al.[16](black points), and the calculations by GEF for J rms = 8 and E x = 6 . shown in Fig. 6 for uranium and Fig. 9 for plutonium.The constant trend (though not the absolute value) inspectral characteristics that we observe is broadly in linewith the predictions with GEF.There seems to be a slight decrease in the ¯ M below S n for both nuclei, but more clearly seen in the pluto-nium data. Although up to 5 MeV of extra excitationenergy for the hot fission fragments is available, this en-ergy is clearly more efficiently dissipated by the evapora-tion of prompt fission neutrons. The prompt fission neu-tron multiplicity is well known to increase linearly withexcitation energy. One could expect that the total angu-lar momentum J of the fissioning nucleus should increasewith increasing E x . Our experimental data exhibit a flattrend, which is compatible to GEF calculations for a con-stant or energy dependent J rms in the studied excitationenergy range.An excess of counts is observed when comparing thesurrogate (d,p) PFG and thermal neutron induced PFGS.Such a discrepancy might arise from differences in thesurrogate and neutron induced reactions. The spectrum(Fig. 10) predicted with the GEF code lies in betweenthe two experimental cases in the region in which thedeviation is observed. For γ -rays above 8 MeV, signifi-cantly less photons are predicted in comparison with ourdata. The spectrum by Verbinski et al. [16] is reportedonly up to E γ =7.5 MeV.It is expected that reactions involving charged particleswill on average introduce more angular momentum L trans into the reaction, than thermal neutron induced reac-tions. The distribution of the angular momentum J willhave a tail, which extends higher, the greater the massdifference is between the ingoing and outgoing chargedparticles in the reaction. It may, therefore, be possiblethat the excess counts observed in the PFGS of the surro-gate reaction is an angular momentum effect introduced by using the (d,p) reaction to induce fission, instead ofneutrons.It is consistent that for ¯ M and E tot our (d,p) PFGdata are in better agreement with larger J rms , whereasthe thermal neutron induced data are in all cases in goodagreement with low J rms . For E av the results of the GEFcalculation are in both reactions less sensitive to J rms ,and there discrepancy between our experimental resultsand the calculations increases.The absolute values of the E tot and the ¯ M are higherfor the U* than the
Pu*. Comparison with theresults from GEF, and a slightly higher deuteron beamenergy, indicates a higher angular momentum in the ura-nium case. Average higher angular momentum of thefission fragments might result in neutron emission be-ing partially hindered from odd fission fragments up to1 MeV above their S n . In such a case γ -ray emissionwill compete with neutron emission, also above S n . Thiswould result in an increased total γ energy and higher¯ M .Recently, surrogate measurements have demonstratedthat radiative capture and fission cross sections [45] canbe used to get quantitative insight into the angular mo-mentum L trans imparted to the compound nucleus follow-ing a specific transfer reaction. A detailed review of boththeory, experimental results and challenges can be foundin Ref. [46]. The connection between these cross sec-tions and L trans involves sophisticated Hauser-Feshbachcalculations [47]. On the other hand, it is establishedthat prompt fission γ multiplicity ¯ M is the most directprobe of the angular momentum of the fission fragments.The latter is influenced by the angular momentum of thefissioning system, i.e. L trans in the presented GEF cal-culations. The present work shows for the first time thatthe measured ¯ M is indeed sensitive to L trans . Hence, itcan be used as an alternative observable, complementaryto cross sections [45], to quantify L trans .Above the neutron binding energy S n there is no sig-nificant increase in average PFG energy and total PFGenergy released per fission with increasing excitation E x .This observation is important for applications, since γ -rays from fission are responsible for a large part of theheating that occurs in reactor cores. The observed resultimplies that passing from current Generation-III ther-mal reactors to fast Generation-IV reactor concepts willnot require significant changes in the modelling of γ heattransport from the fast neutron induced fission process.Since U is the main fissile isotope in the thorium cy-cle, and
Pu is the main fissile isotope in the pluto-nium/uranium cycle, and the flat trend is observed inboth these nuclei, effects of γ heating from fission in bothcycles are expected to be similar. VI. CONCLUSION
Emission of prompt γ -rays from nuclear fission inducedvia the U(d,pf) and
Pu(d,pf) reactions have beenstudied. PFGS have been extracted as functions of thecompound nucleus excitation energy for both nuclei. Theaverage spectral characteristics have been deduced andtrends as a function of excitation energy have been stud-ied and compared with calculations by the GEF code.We observe an approximately constant behaviour ofthe spectral properties as a function of energy for bothnuclei. However, a much lower multiplicity is seen in thesub-barrier fission of
Pu*. More detailed studies areneeded to understand why sub-barrier fission results inemission of low multiplicities of prompt γ -rays from theexcited fission fragments. Furthermore, we observe anexcess of γ -rays above 2 MeV emitted in the surrogate Pu(d,pf) reaction when comparing to the neutron in-duced PFGS measured by Verbinski et al. This effect isnot yet understood, but may be as due to higher angu-lar momenta involved in the transfer-induced reactionsas compared to the neutron-induced one, over the energyrange of our study. This conjecture is supported by GEFcalculations.Our measured γ ray multiplicities and total γ energiesare higher than those observed for the neutron inducedreactions from Verbinski et al. and Pleasonton. Thisdifference may be explained as due to higher J by com-paring to the GEF calculations.In the future we hope to revisit these types of measure-ments with the OSCAR array of 26 large volume LaBr detectors currently being constructed at the Oslo Cy-clotron Laboratory. These will not only provide a muchbetter γ -ray energy resolution and lower energy thresh- olds, but an excellent timing resolution which will allowfor discrimination of neutrons from γ -rays via time offlight. ACKNOWLEDGMENTS
We would like to thank J. M¨uller, E. A. Olsen, andA. Semchenkov for providing excellent beams during theexperiments.We would also like to thank Beatriz Juradoand Karl-Heinz Schmidt for fruitful discussions. A.C.Larsen gratefully acknowledges funding through ERC-STG-2014, grant agreement no. 637686. G.M.T. andS. Siem gratefully acknowledge funding through the Re-search Council of Norway, Project No. 222287 andgrant no. 210007, respectively. We would like to thankLawrence Livermore National Laboratory for providingthe
U and
Pu targets. This work was performedunder the auspices of the University of California Of-fice of the President Laboratory Fees Research Pro-gram under Award No. 12-LR-238745, the U.S. Depart-ment of Energy by Lawrence Livermore National Labo-ratory under Contract DE-AC52-07NA27344, LawrenceBerkeley National Laboratory under Contract No. DE-AC02-05CH11231, and the National Research Founda-tion of South Africa under Grant Nos. 92789 and 83671.M.Wiedeking acknowledges funding from the NationalResearch Foundation of South Africa under Grant Nos.92989 and 83867. [1] L. Meitner and O. R. Frisch, Nature , 239240 (1939).[2] O. Hahn and F. Strassmann, Die Naturwissenschaften , 11 (1939).[3] N. Bohr and J. A. Wheeler, Physical Review , 426450(1939).[4] F. Pleasonton, R. L. Ferguson, and H. Schmitt, PhysicalReview C , 1023 (1972).[5] H. Bowman and S. Thompson, The prompt radiations inthe spontaneouos fission of Cf , Tech. Rep. (California.Univ., Livermore. Radiation Lab., 1958).[6] H. 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