Total Absorption Spectroscopy Study of 92 Rb Decay: A Major Contributor to Reactor Antineutrino Spectrum Shape
A.-A. Zakari-Issoufou, M. Fallot, A. Porta, A. Algora, J.L. Tain, E. Valencia, S. Rice, V.M Bui, S. Cormon, M. Estienne, J. Agramunt, J. Äystö, M. Bowry, J.A. Briz, R. Caballero-Folch, D. Cano-Ott, A. Cucoanes, V.-V. Elomaa, T. Eronen, E. Estévez, G.F. Farrelly, A.R. Garcia, W. Gelletly, M.B Gomez-Hornillos, V. Gorlychev, J. Hakala, A. Jokinen, M.D. Jordan, A. Kankainen, P. Karvonen, V.S. Kolhinen, F.G Kondev, T. Martinez, E. Mendoza, F. Molina, I. Moore, A.B. Perez-Cerdán, Zs. Podolyák, H. Penttilä, P.H. Regan, M. Reponen, J. Rissanen, B. Rubio, T. Shiba, A.A. Sonzogni, C. Weber, IGISOL collaboration
TTotal Absorption Spectroscopy Study of Rb Decay: A Major Contributor to ReactorAntineutrino Spectrum Shape
A.-A. Zakari-Issoufou, M. Fallot, A. Porta, A. Algora,
2, 3
J.L. Tain, E. Valencia, S. Rice, V.MBui, S. Cormon, M. Estienne, J. Agramunt, J. ¨Ayst¨o, M. Bowry, J.A. Briz, R. Caballero-Folch, D. Cano-Ott, A. Cucoanes, V.-V. Elomaa, T. Eronen, E. Est´evez, G.F. Farrelly, A.R. Garcia, W. Gelletly,
2, 4
M.B Gomez-Hornillos, V. Gorlychev, J. Hakala, A. Jokinen, M.D. Jordan, A.Kankainen, P. Karvonen, V.S. Kolhinen, F.G Kondev, T. Martinez, E. Mendoza, F. Molina,
2, 10
I. Moore, A. B. Perez-Cerd´an, Zs. Podoly´ak, H. Penttil¨a, P.H. Regan,
4, 11
M. Reponen,
8, 12
J. Rissanen, B. Rubio, T. Shiba, A.A. Sonzogni, C. Weber,
8, 14 and IGISOL Collaboration SUBATECH, CNRS/IN2P3, Universit´e de Nantes,Ecole des Mines de Nantes, F-44307 Nantes, France Instituto de Fsica Corpuscular (CSIC-Universitat de Valencia),Apartado Correos 22085, E-46071 Valencia, Spain Institute of Nuclear Research, MTA ATOMKI, Debrecen, 4026 Hungary Department of Physics, University of Surrey, Guildford GU27XH, United Kingdom Helsinki Institute of Physics, University of Helsinki, FI-00014 Helsinki, Finland Universitat Polit´ecnica de Catalunya (UPC), 08034 Barcelona, Spain Centro de Investigaciones Energticas Medioambientales Y Tecnolgicas, E-28040 Madrid, Spain Department of Physics, University of Jyv¨askyl¨a, P.O. Box 35, FI-40014 Jyv¨askyl¨a, Finland Argonne National Laboratory, Argonne, IL 60439, USA Present address: Comisi´on Chilena de Energ´ıa Nuclear, Post Office Box 188-D, Santiago, Chile National Physical Laboratory, Teddington, Middlesex, TW11 0LW, United Kingdom Present address: RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan National Nuclear Data Center, Brookhaven National Laboratory, Upton NY 11973-5000, USA Present address: Faculty of Physics, Ludwig-Maximilians University Munich,Am Coulombwall 1, D-85748 Garching, Germany (Dated: September 25, 2015)The antineutrino spectra measured in recent experiments at reactors are inconsistent with calcu-lations based on the conversion of integral beta spectra recorded at the ILL reactor. Rb makesthe dominant contribution to the reactor antineutrino spectrum in the 5-8 MeV range but its decayproperties are in question. We have studied Rb decay with total absorption spectroscopy. Previ-ously unobserved beta feeding was seen in the 4.5-5.5 region and the GS to GS feeding was foundto be 87.5(25)%. The impact on the reactor antineutrino spectra calculated with the summationmethod is shown and discussed.
Beta decay properties of fission products are at theorigin of the antineutrino flux emitted by reactor cores.This flux has been used for decades as a source for reactorneutrino experiments, such as Daya Bay, Double Choozand Reno which have recently published their new resultsfor the mixing angle θ [1–3]. These results will allowfuture searches for the CP violation phase δ or the neu-trino mass hierarchy with complementary experimentsat reactors [4]. The accurate determination and under-standing of the emitted reactor antineutrino flux is thusstill required for present and future experiments. Therecent re-estimate of reactor antineutrino energy spec-tra [5, 6] has led to the so-called “reactor anomaly” [7],at the origin of new experimental projects chasing shortdistance oscillations at research reactors [8]. These calcu-lations are based on the conversion into antineutrinos ofthe only available measurement of the beta energy spec-tra performed using the high flux reactor at the Insti-tut Laue-Langevin (ILL) in Grenoble, France [9]. Theconversion method has until now been considered as themost precise one by experimenters studying neutrino os- cillations. But recently, Hayes et al. [10] have shown thatit is dependent on the underlying nuclear physics andthat the associated errors should be revised. In addition,very recent experimental results from [1–3] have shownan unexplained distortion between 4 and 8 MeV in theirmeasured positron energy spectra from Pressurized Wa-ter Reactors (PWR) [11] with respect to the convertedspectra [5, 6] (an excess of ca. 10% over 2 MeV followedby a dip). The positron energy used in reactor antineu-trino experiments corresponds to the antineutrino energyminus the mass difference between the neutron and pro-ton. In this context, new evaluations of PWR antineu-trino energy spectrum are essential.An alternative method, independent of the ILL mea-surements, relies on the summation of the contributionsof the fission product beta decay branches to obtain theantineutrino energy spectra. The need to measure newnuclear physics properties of some major contributors tothe antineutrino spectrum was underlined in [12], whereit was shown that we should use the Total AbsorptionSpectroscopy (TAS) technique to avoid the pandemo- a r X i v : . [ nu c l - e x ] S e p nium effect [13] and improve the predictions of the sum-mation method. The summation method is indeed theonly one which allows the prediction of antineutrino spec-tra for which no integral beta measurement exists. Thisis required, for instance, in the context of the R&D of an-tineutrino detection as a tool for reactor monitoring [14].In this Letter, we present the first results of an exper-imental campaign performed with TAS technique [15]aimed at the measurement of beta decay properties ofimportant contributors to the reactor antineutrino en-ergy spectrum emitted by PWRs. In particular, we shownew results for Rb, the largest contributor to the reac-tor antineutrino flux in the energy range above 5 MeV. Inthe following, we present a short list of nuclei making themain contributions to the antineutrino energy spectrumabove 4 MeV, obtained using the summation method pre-sented in [12]. Then, previous experimental knowledge ofthe beta decay properties of Rb is summarized, and theTAS method, the experimental setup used and the dataanalysis performed are presented. Finally, we show thebeta feeding obtained and present the impact of the newresults on reactor antineutrino energy spectra.The main contributors to the antineutrino energy spec-tra from 4 to 8 MeV are listed in Table I. In our calcula-tion, we have chosen to minimize the impact of the pan-demonium effect on the antineutrino spectra and on thecomputed proportions of the nuclei per energy bin. Forthis purpose, we have used data from [16] for , , Rb, Y, Cs,
Te and from [17] for Sr and Rb, be-cause these two sets of data are likely to be pandemo-nium free (though they may suffer from other systematicerrors). As they were not measured by [17] or [16], datafor m Y and
Nb were taken from [18] and m Nbfrom [19]. Indeed, a careful choice of data sets is needed,especially to select nuclei which would deserve new mea-surements, as is illustrated below with the case of Rb.Note that in the 4 to 6 MeV range, unknown nuclei re-quiring the use of models represent less than 1% of thespectrum, while they represent about 4% of the 7 to8 MeV bin. Rb makes the main contribution between 4 to 8 MeV,representing alone up to about 38 % of the 7 to 8 MeVbin and 16 % of the 5 to 8 MeV range. Rb is quitecontroversial: the beta feeding to the ground state of itsdaughter nucleus, Sr, was fixed at 51% ±
18% in theENSDF data base [20] until 2012, before the inclusion inthe references of the article from Lhersonneau et al. [21],which concluded that close to half of the decay intensity,mostly high energy ground state transitions, is missingin the decay scheme. Following this reference the betafeeding to the ground state of Sr was recently changedto 95.2 % ± .
7% in the ENSDF database [19]. Rb has a large Q β value which makes it a goodcandidate to be a pandemonium nucleus. The pande-monium effect [13] arises from the difficulty encounteredin building level schemes for complex beta decays using Germanium detectors, especially when beta transitionsoccur to high-energy levels or regions of high level den-sity. This leads to an underestimate of the correspond-ing beta branches to states at high excitation energy andthus to a distortion in the beta decay feeding. In addi-tion, Rb has also been used as a critical example [22]to show how beta-decay strength calculations impact onthe predictive power of models in reconstructing half-lives and beta-delayed neutron emission probabilities ofnuclei, whose properties are important in the simulationof the astrophysical r-process. It is also on NEA/IAEAlists of important contributors to reactor decay heat [23].A total absorption spectrometer is a calorimeter mea-suring the gamma cascades emitted by the deexcitationof the daughter nucleus after beta decay of the parent.The detection of the total energy allows the deduction ofthe feeding probability of excited levels populated in thebeta decay. This quantity is calculated by solving the“inverse problem” as presented below. The beta feeding f gives direct access to the beta intensity I i = f i / Σ k f k and then to the beta strength, a microscopic quantitythat can be directly compared with models [24]. Thedetector used in the measurement of the Rb decay iscomposed of 12 crystals of BaF arranged in a compactgeometry described in [25]. Each crystal is coupled toa photomultiplier tube converting the scintillation lightinto an electrical signal directly proportional to the de-tected energy. The gamma detection efficiency was ∼
80 % at 5 MeV. This spectrometer was coupled to a sili-con detector placed in the center, behind the source im-plantation zone, to tag the beta emission. This reducesthe background by demanding coincidences between betaevents and the following gamma emission from deexcita-tion of levels in the daughter.
TABLE I. Main contributors to a standard PWR antineu-trino energy spectrum computed with the MURE code cou-pled with the list of nuclear data given in [12], assuming thatthey have been emitted by
U (52%),
Pu (33%),
Pu(6%)and
U (8.7%) for a 450 day irradiation time and usingthe summation method described in [12].4 - 5 MeV 5 - 6 MeV 6 - 7 MeV 7 - 8 MeV Rb 4.74% 11.49% 24.27% 37.98% Y 5.56% 10.75% 14.10% -
Cs 3.35% 6.02% 7.93% 3.52%
Nb 5.52% 6.03% - - Rb 2.34% 4.17% 6.78% 4.21% m Y 2.43% 3.16% 4.57% 4.95%
Te 4.01% 3.58% - - m Nb 0.72% 1.82% 4.15% 7.76% Rb 1.90% 2.59% 1.40% - Sr 2.65% 2.96% - - Rb 1.32% 2.06% 2.84% 3.96% Rb ions were produced via proton-induced fission onan uranium target at the IGISOL facility [26] in the ac-celerator Laboratory of the University of Jyv¨askyl¨a (Fin-land). JYFLTRAP double Penning trap [27] was usedfor selecting with high precision only Rb ions using themass-selective buffer gas cooling technique [28]. Thishigh level of purification of the beam is necessary in TASexperiments in order to reduce systematic uncertaintiesrelated to the purity of the beam.As stated above the main observable in a TAS mea-surement is the beta feeding to the energy levels of thedaughter nucleus which is contained in the measuredgamma spectrum convoluted with the detector response.To extract this information we have to solve the so-called“inverse problem”. It consists of solving the equation d i = R ( B ) ij × f j , where R ( B ) ij is the response matrix of thedetector to an assumed decay level scheme ( B ). R ij con-nects feeding to level j ( f j ) to counts in the bin i of the“measured” TAS spectrum ( d i ). The analysis procedurehas been described in previous publications [24, 29] andis well understood.To perform the analysis, very clean decay data d arerequired. Possible contamination from the daughter nu-clei decay and pileup signals are subtracted from the rawdata. The shape of the pile-up spectrum has been com-puted by summing in the ADC time window two eventsrandomly extracted from the raw data. The absolutenormalization of the pileup was performed using the datacounting rate and the ADC time window in which ran-dom coincidences can occur [30, 31]. The shape of thespectrum from the decay of the daughter nucleus Srhas been simulated using its known level scheme fromENSDF [19] and the detector response. The normal-ization factor has been obtained solving the Batemanequations for the decay of Rb in realistic experimen-tal conditions, i.e. considering the experimental time forimplantation and measuring cycles. The contaminationfrom Sr decay represents 0.08 % of the total Rb dataacquired. The response matrix R is calculated by simu-lating the detector response to beta and gamma cascadesemitted during the decay with a dedicated GEANT4 [32]Monte Carlo simulation. The latter has been validatedusing measurements performed with known sources inorder to reproduce the detector response in great detail[30, 33, 34]. The “inverse problem” is solved by using amaximization expectation algorithm based on the Bayestheorem and combined with a χ minimization [35]. Itmakes use of an iterative method to find the final feedingdistribution by minimizing the difference between the ex-perimental data and the spectrum recreated by the resultof the algorithm at each iteration. The analysis startswith a first guess at feeding values extracted from theliterature, or an equally probable feeding distribution ifthe nucleus is poorly known, and stops when the χ valuededuced from the two spectra is at a minimum.The starting point for solving the inverse problem is the construction of the branching ratio matrix ( B ) for thestates populated in the decay. For this purpose we beginby using the known information, derived from high reso-lution studies, about levels up to an excitation energy of1778 keV in Sr [19]. Above this energy little is knownand the data are divided into 40 keV bins up to the Q β value. In this range we must have recourse to semiem-pirical statistical models and we must supply as inputboth the level densities and gamma strength functions.Three level-density models were tested: Back-Shifted-Fermi-Gas (BSFG) [36, 37], Constant-Temperature [37],and Gilbert-Cameron models [38]. The last of these isa combination of the other two. The Gilbert-Cameronformulation was chosen because it best reproduces theexperimental data at low energies. The gamma strengthswere modeled with a Lorentz function using the param-eters given in [39]. In determining the β -feeding distri-bution, it is possible to fix or vary the feeding to eachindividual level or energy bin. The feeding to the 1673.3keV level was set to zero, since the probable spin parityis 4 + and any feeding from the Rb ground state mustbe negligible.The reconstructed spectrum (blue dashed line) calcu-lated using the feeding distribution obtained from thisanalysis is compared with the clean decay data (blackcontinuous line) of Rb in the upper panel of figure 1[30]. The lower panel shows the residues between thesetwo curves. The beta intensity obtained from the so-lution of the inverse problem for Rb is shown in fig-ure 2 in the blue continuous line, while the red dashedlines are the intensities from ENSDF [19]. As the groundstate feeding is very important in the case of the decayof Rb, we have estimated the main errors involved inthis reconstruction [30]. They are listed as follows: thethreshold of the beta spectrum, statistical uncertainty,error induced by pile-up subtraction, errors in the detec-tor energy calibration and resolution used in the calcu-lation of the response matrix R and errors obtained bytesting different input parameters for the calculation of R and inverse problem resolution. A sum in quadratureof all the systematic and statistical errors quoted abovegives a 2.5 % error on the ground state feeding. This re-sult is conservative, as we have voluntarily adopted largevalues of the main errors which are associated with thethreshold of the beta spectrum and with the choice ofmodel for the level density. The TAS results show somebeta intensity around 4.5 and 5.5 MeV which was notdetected before. The intensity to the ground state ob-tained from our analysis is 87.5 (25) %. This value canbe obtained from the data analysis because the TAS de-tector also measures the bremsstrahlung radiation fromthe beta particles. These events are in the low energypart of the measured spectrum and, since they are con-sidered in the response matrix R , they contribute to thereconstruction of the spectrum and, then, in the calcula-tion of beta feeding. The selected ground state feeding is E[keV] 0 1000 2000 3000 4000 5000 6000 7000 8000 C oun t s
10 tagged b Rb: TAS Experiment Recalculated
Energy [keV] 0 1000 2000 3000 4000 5000 6000 7000 8000 R e s i due [ % ] - - - - FIG. 1. Upper panel: Comparison between measured spec-trum (black continuous line) and reconstructed one (bluedashed line) with the feeding obtained from the TAS dataanalysis. Lower panel: Residues between the two curves re-ported in the upper panel.
Energy [keV] I[ % ] fl n S fl b Q Rb: -tagged b :TAS Experiment :ENSDF (High resolution) FIG. 2. Beta intensity for the decay of Rb obtained withTAS measurements in the blue continuous line. Red dashedlines are data from ENSDF [19]. Ground state feeding fromENSDF is 95 . ± .
7% , while from this work it is 87 . ± . the one which minimizes the χ value determined fromthe experimental data and the reconstructed spectrumafter the analysis. If we fix the ground state feeding tobe 95.2 % as reported in the ENSDF data base [19] ouranalysis converges with a χ value of 2048 which is muchlarger than the minimum of 630, completely excludingthis hypothesis.The antineutrino energy spectrum emitted in Rbbeta decay has been computed using the beta feeding pre-sented above. The GS to GS transition is first-forbiddennonunique (spin parity of Rb 0 − ). Different spectralshapes were assumed for this transition, considering thedifferent possibilities listed in [10]; an allowed shape, afirst forbidden nonunique shape due to the GT operator and a first forbidden nonunique shape due to the ρ A oper-ator. It was also assumed that the remaining transitionswere of allowed or first forbidden unique type. The vari-ous combinations of these options were computed and theshapes obtained were very similar. No significant impactis expected from the uncertainty of the shape of the firstforbidden nonunique GS to GS transition. We chose toadopt an allowed shape for the GS to GS transition andfirst forbidden unique shapes for the remaining branchesdue to the spins and parities of the known transitions inthis nucleus.The antineutrino energy spectra were calculated withthe summation method described in [12]. In [12] the dataadopted for Rb were extracted from [16]. In principle,these measurements should not suffer from the pandemo-nium effect, nor from a lack of knowledge of the types ofthe beta transitions. Unfortunately, however, the errorbars are quite large. In figure 3, the ratio between the an-tineutrino spectra of , Pu and , U from [12] andthose obtained using our new results for Rb is displayedwith the red dashed-dotted line. As expected, the maineffect is in the 4 to 8 MeV antineutrino energy range,with a maximum between 7 and 8 MeV, and amounts to4.5% for
U, 3.5% for
Pu, 2% for
Pu and 1.5% for
U. These discrepancies are due to the difference in theshapes of the antineutrino spectra built with the newlymeasured beta feedings with respect to the antineutrinospectra converted from Rudstam’s measurements. Thecomparison would be very similar if we had used the lat-est ENSDF [19] data for Rb in our summation calcula-tions, as was done in [40]. The ratio is displayed as well inFig. 3 with green dotted lines, and is nearly superposedon the ratio built when using Rudstam data in the firstplace. The change becomes even more dramatic if onecompares with summation method spectra in which anolder version of the ENSDF data was used, as in [41]. Thelatter ratio is plotted with black dashed lines in figure 3.This shows the relevance of the present Rb decay datain the calculations.In summary, the results of new measurements of thebeta decay properties of Rb have been presented.This nucleus makes one of the largest contributionsto the emitted antineutrino flux by standard thermalreactors in the energy region above 5 MeV. The mea-surements have been performed using pure isotopicbeams and the TAS technique to provide data freefrom the pandemonium effect. The measured feedingdistribution, which extends to states previously not seenin high-resolution measurements and also determines theGS to GS feeeding as 87.5(25)%, confirms the relevanceof this decay to antineutrino summation calculations.The impact of the measurements has been evaluatedby comparing the ratio of summation calculations usingthe new feeding distribution with the results using thefeeding distributions employed in [12, 40, 41]. The effectof introducing the new results is particularly marked in
Energy (MeV) R a t i o ( w / w o ne w da t a ) U U U Energy (MeV) R a t i o ( w / w o ne w da t a ) U U U Energy (MeV) R a t i o ( w / w o ne w da t a ) Pu Pu Pu Energy (MeV) R a t i o ( w / w o ne w da t a ) Pu Pu Pu R a t i o ( w / w o ne w da t a ) Energy (MeV)
FIG. 3. Ratio between the antineutrino spectra calculatedusing the results presented in this paper with respect to thedata on Rb decay used in [12] (thick red dashed-dotted line),in [40] (green dotted line) and in [41] (black dashed line). Thesharp drop in the ratio, in one single bin located at the Qvalue of the Rb, is due to the different values in Q givenin [16] and [19], that were used to reconstruct the antineu-trino spectrum. A gray horizontal bar is placed above theantineutrino energy scale to indicate the region of the distor-tion observed by the reactor antineutrino experiments whitrespect to converted spectra. the case of [41] and calls for a revision of the conclusionsdrawn in that paper. It is clear that this is becausethe GS to GS feeding used in [41] was incorrect. Theoverall agreement of the new summation calculationswith the converted spectra [6] is improved in the 4to 8 MeV range except in the case of
U for whichthe summation method spectrum is always below theconverted spectrum. The change is especially striking inthe case of [41] in the 5 to 8 MeV antineutrino energyrange, which overlaps the energy region in which reactorneutrino experiments have shown a spectral distor-tion [11]. It also shows that the inclusion of all existingTAS nuclear data (ca. 37 nuclei) in [41]’s calculation maychange dramatically the spectral shape they compute.Overall, this emphasizes why new measurements areneeded for the radioactive decays of importance inthe reactor antineutrino spectrum and, in particular,why measurements should be performed with the totalabsorption method. The present measurement, whichreduces significantly the uncertainties associated withthe antineutrino summation calculations in the 4 to8 MeV range, is an important step towards better pre-dictions with the summation method. Provided that inthe 4 to 6 MeV range, unknown nuclei requiring the useof models represent less than 1% of the spectrum in the summation calculation from [12], one can thus expect adramatic reduction of the final uncertainty in this rangeas a long term result of the TAS campaign. In parallel,the impact of the uncertainties of the fission yields onthe antineutrino spectrum needs to be evaluated moreaccurately.This work was supported by the CHANDA Euro-pean Project, the PICS 05761 between CNRS/in2p3and CSIC, the GEDEPEON research groupment, theNEEDS challenge and STFC (UK).This work was supported by Spanish Ministeriode Econom´ıa y Competitividad under Grants No.FPA2008-06419, FPA2010-17142 and FPA2011-24553,and CPAN CSD-2007-00042 (Ingenio2010).Work at ANL was supported by the U.S. DOE, Officeof Nuclear Physics under Contract No. DE-AC02-06CH11357. [1] Y. Abe et al. (Double Chooz Collaboration), Phys. Rev.D , 052008 (2012).[2] F. P. An et al. (Daya Bay Collaboration), Phys. Rev.Lett. , 171803 (2012).[3] J. K. Ahn et al. (Reno Collaboration), Phys. Rev. Lett. , 191802 (2012).[4] L. Yu-Feng, Int. J. Mod. Phys. Conf. Ser. , 1460300(2014).[5] Th. A. Mueller et al., Phys. Rev. C , 054615 (2011).[6] P. Huber, Phys. Rev. C , 024617 (2011).[7] G. Mention et al., Phys. Rev. D , 073006 (2011).[8] K. N. Abazajian et al., “Light sterile neutrino: a whitepaper,” arXiv:1204.5379v1 [hep-ph] (2012).[9] A. A. Hahn et al., Phys. Lett. B , 365 (1989).[10] A. C. Hayes, J. L. Friar, G. T. Garvey, G. Jungman, andG. Jonkmans, Phys. Rev. Lett. , 202501 (2014).[11] Double Chooz and Reno Collaborations inProceedings of the Neutrino 2014 Conferencehttp://neutrino2014.bu.edu/, Daya Bay Collabora-tion in Proceedings of the ICHEP 2014 Conference,http://ichep2014.es/.[12] M. Fallot et al., Phys. Rev. Lett. , 202504 (2012).[13] J. C. Hardy, L. C. Carraz, B. Jonson, and P. G. Hansen,Phyics Letter B , 307 (1977).[14] M. Fallot et al., Nucl. Data Sheets , 137 (2014).[15] M. Fallot, J. L.. Tain, A. Algora, et al., “Study of nu-clei relevant for precise predictions of reactor neutrinospectra,” Experiment proposal to the PAC of Jyv¨askyl¨a(2009).[16] G. Rudstam et al., At. Data and Nucl. Data Tables ,239 (1990).[17] R. C. Greenwood, R. G. Helmer, M. H. Putnam, andK. Watt, Nucl. Instrum and Methods Phys. Res. Sect. A , 2187 (2012).[20] C. Baglin, Nucl. Data Sheets , 423 (2000).[21] G. Lhersonneau et al., Phys. Rev. C , 017308 (2006). [22] P. M¨oller, B. Pfeiffer, and K.-L. Kratz, Phys. Rev. C ,055802 (2003).[23] Assessment of Fission Product Decay Data for De-cay Heat Calculations, Nuclear Science NEA/WPEC-25 (2007). Decay Heat Calculation: Assessment of Fis-sion Product Decay Data Requirements for Th/U Fuel,INDC(NDS)-0577 (2010).[24] D. Jordan et al., Phys. Rev. C , 044318 (2013).[25] A. Algora et al., Nucl. Data Sheets , 12 (2014).[26] I. D. Moore et al., Hyperfine Interact. , 17 (2014).[27] T. Eronen et al., Eur. Phys. J. A , 46 (2012).[28] G. Savard et al., Phys. Lett. A , 247 (1991).[29] A. Algora et al., Phys. Rev. Lett. , 202501 (2010).[30] A.-A. Zakari, Ph.D. thesis, Universit´e Nantes, France(2015).[31] D. Cano-Ott et al., Nucl. Instrum Methods Phys. Res.Sect. A , 488 (1999). [32] http://geant4.cern.ch/.[33] S. Rice, Ph.D. thesis, University of Surrey, UK (2014).[34] D. Cano-Ott et al., Nucl. Instrum. Methods Phys. Res.Sect. A , 333 (1999).[35] J. L. Tain et al., Nucl. Instrum. Methods. Phys. Res.Sect. A , 728 (2007).[36] W. Dilg, W. Schantl, H. Vonach, and M. Uhl, Nucl.Phys. A , 269 (1973).[37] T. von Egidy and D. Bucurescu, Phys. Rev. C , 044311(2005).[38] A. Gilbert and A. G. W. Cameron, Can. J. Phys. , 011301 (R) (2015).[41] D. A. Dwyer and T. J. Langford, Phys. Rev. Lett.114