Extensive study of the quality of fission yields from experiment, evaluation and GEF for antineutrino studies and applications
K.-H. Schmidt, M. Estienne, M. Fallot, S. Cormon, A. Cucoanes, B. Jurado, K. Kern, Ch. Schmitt, T. Shiba
EExtensive study of the quality of fission yieldsfrom experiment, evaluation and GEFfor antineutrino studies and applications
K.-H. Schmidt, ∗ M. Estienne, † M. Fallot, S. Cormon, A. Cucoanes, and T. Shiba
Subatech, CNRS/IN2P3-Universit´e de Nantes-IMTA4 rue Alfred Kastler, F-44307 Nantes, France
B. Jurado
CENBG, CNRS/IN2P3, Chemin du Solarium B.P. 120, F-33175 Gradignan, France
K. Kern
Prokerno Corp., Apartado Postal 0823-04789, Panam´a - Bella Vista, Republic of Panama
Ch. Schmitt
IPHC, CNRS/IN2P3, 23 rue du Loess, B.P. 28, F-67037 Strasbourg, France
Abstract:
The understanding of the antineutrino production in fission and the theoretical cal-culation of the antineutrino energy spectra in different, also future, types of fission reactors relyon the application of the summation method, where the individual contributions from the differentradioactive nuclides that undergo a beta decay are estimated and summed up. The most accurateestimation of the independent fission-product yields is essential to this calculation. This is a complextask, because the yields depend on the fissioning nucleus and on the energy spectrum of the incidentneutrons.In the present contribution, the quality of different sources of information on the fission yields isinvestigated, and the benefit of a combined analysis is demonstrated. The influence on antineutrinopredictions is discussed.In a systematic comparison, the qualilty of fission-product yields emerging from different exper-imental techniques is analyzed. The traditional radiochemical method, which is almost exclusivelyused for evaluations, provides an unambiguous identification in Z and A , but it is restricted toa limited number of suitable targets, is slow, and the accuracy suffers from uncertainties in thespectroscopic nuclear properties. Experiments with powerful spectrometers, for example at LO-HENGRIN, provide very accurate mass yields and a Z resolution for light fission products fromthermal-neutron-induced fission of a few suitable target nuclei.On the theoretical side, the general fission model GEF has been developed. It combines a fewgeneral theorems, rules and ideas with empirical knowledge. GEF covers almost all fission observ-ables and is able to reproduce measured data with high accuracy while having remarkable predictivepower by establishing and exploiting unexpected systematics and hidden regularities in the fissionobservables. In this article, we have coupled for the first time the GEF predictions for the fissionyields to fission-product beta-decay data in a summation calculation of reactor antineutrino energyspectra. The first comparisons performed between the spectra from GEF and those obtained withthe evaluated nuclear databases exhibited large discrepancies that highlighted the exigency of themodelisation of the antineutrino spectra and showing their usefulness in the evaluation of nucleardata. Additional constraints for the GEF model were thus needed in order to reach the level ofaccuracy required by the antineutrino energy spectra. The combination of a careful study of theindependent isotopic yields and the adjunction of the LOHENGRIN fission-yield data as additionalconstraints led to a substantially improved agreement between the antineutrino spectra computedwith GEF and with the evaluated data. The comparison of inverse beta-decay yields computed withGEF with those measured by the Daya Bay experiment shows the excellent level of predictivenessof the GEF model for the fundamental or applied antineutrino physics.The main results of this study are:- an improved agreement between the antineutrino energy spectra obtained with the newly tunedGEF model and the JEFF-3.1.1 and JEFF-3.3 fission yields for the four main contributors to fissionin standard power reactors; a r X i v : . [ nu c l - e x ] D ec indications for shortcomings of mass yields for Pu(n th ,f) and other systems in current evalu-ations;- a demonstration of the benefit from cross-checking the results of different experimental ap-proaches and GEF for improving the quality of nuclear data;- an analysis of the sources of uncertainties and erroneous results from different experimentalapproaches;- the capacity of GEF for predicting the fission yields (and other observables) in cases (in termsof fissioning systems and excitation energies) which are presently not accessible to experiment;- predictions of antineutrino energy spectra that aim to assess the prospects for reactor monitoring,based on the GEF fission yields associated with the beta-decay data of the most recent summationmodel. ∗ † Corresponding author: [email protected] ONTENTS
I. Introduction 5II. The GEF model 6A. Concept 6B. Strengths and weaknesses 8III. GEF improvements using reactor antineutrinos and application to antineutrino production 8A. Summation calculations for antineutrinos 8B. Sensitivity of antineutrino spectra to the fission yields 9C. Parameter values 9IV. Experimental approaches 10A. Radiochemistry 111. The method 112. Independent and cumulative yields 113. Yields of short-lived products 114. Strengths and weaknesses 12B. Experiments with particle detectors in direct kinematics 121. The method 122. Strengths and weaknesses 12C. Experiments with particle detectors in inverse kinematics 131. The method 132. Strengths and weaknesses 13V. Evaluations 13VI. Comparative study 13A. Overall impression 131. Illustrative cases 142. Treatment of energy distributions: the case of
U(n fast ,f) 36B. Problems and proposed solutions 381. A =129 yield of U(n th ,f) 392. Mass yields of Th(n th ,f) 413. Mass yields of U(n th ,f) 414. Mass yields of U(n th ,f) 425. Mass yields of Np(n th ,f) 436. Mass yields of Pu(n th ,f) 447. Mass yields of Cf(n th ,f) 458. Mass yields of Es(n th ,f) 469. Mass yields of Fm(n th ,f) 48C. Quantitative analysis 48D. Summary 48VII. Predictions of antineutrino energy spectra based on the GEF fission yields 50A. Beta-decay emitters 50B. Antineutrino energy spectra 52C. Sensitivity to the fission product distributions from different systems 58VIII. Conclusion 59Acknowledgement 60IX. Appendix 61Observations 61 U(n th ,f) 61 U(n fast ,f) 613 Pu(n th ,f) 62 Pu(n th ,f) 87Summary 87References 874 INTRODUCTION
I. INTRODUCTION
When a heavy nucleus breaks apart, the two fragments, even after prompt-neutron emission, are usually situated onthe neutron-rich side of the nuclear chart. Thus, most of them undergo a sequence of several beta-minus decays, untilthe beta-stability line is reached. In each beta decay, an antineutrino is produced. Each beta emitter is characterizedby a specific antineutrino spectrum, which is determined by the beta Q value and the relative population of groundand excited states in the respective daughter nucleus. Fission reactors form particularly strong antineutrino sources[1], which can be used for particle physics studies [2–5] or for technical purposes. The total spectrum of all thesecontributions from all the fissioning species in a fission reactor is characteristic for the operation method of the reactorand was proposed to be exploited for reactor monitoring [6].Until recently, integral measurements of the beta spectra [7–10] of the main fission sources of a power reactor, U, Pu,
Pu and
U [11], were used to obtain the antineutrino emission by the reactor-neutrino experiments. In 2011,these converted spectra were computed again, and the comparison between the newly obtained predictions and reactorantineutrino experiment results showed a 6% discrepancy [12, 13] called the ”reactor anomaly” [14]. A little later, ashape discrepancy between 5 and 7 MeV in antineutrino energy was evidenced between measured antineutrino spectraand the same predictions, called the shape anomaly [15]. These unexplained discrepancies triggered numerous studiesin several directions: search for sterile neutrinos at reactors [14, 16] ; exploration of potential biases of the conversionmodel [17–19] ; development of an alternative model based on nuclear data i.e. the summation method [12, 20–23].An important pre-requisite of a summation calculation of these antineutrino spectra is an accurate estimation of theindependent fission-product yields, that means the yields before beta decay. The crucial importance of this point isdemonstrated by the considerably diverging antineutrino spectra obtained by using different evaluations [24–27]. Inparticular, drastic discrepancies were found in the antineutrino spectrum, which amount to more than 30% around 5 to6 MeV for
U(n th ,f) when using fission yields from ENDF/B-VII.1, JEFF-3.1.1 and JENDL-4.0, respectively. Alsoproducts with small yields can have strong influence on the antineutrino spectrum, because only few beta emittersmay contribute to certain regions in the antineutrino spectrum.In the present contribution, we investigate how a combined analysis of experiment, evaluation and theory can leadto an improved quality of fission-product yield estimations. In particular, we add the antineutrino observable to theones already used such as decay heat, delayed neutron fractions or prompt neutron multiplicities, and we demonstratethe benefit of including a theoretical model in this process. The GEF model [28] seems to us best suited for thispurpose. The calculation of antineutrino energy spectra with fission yields resulting from different sets of parametersof the GEF model allows tuning these parameters to better reproduce those computed with the JEFF fission yieldswith the constraint to keep the consistency of the parameters among the various fissioning systems.Antineutrino detection for reactor monitoring is another motivation for improving the quality of the fission yieldsstored in the evaluated databases for fission products and of the beta-decay properties. The property of antineutrinosof crossing large quantities of matter without interaction makes them a naturally temper-proof probe. The detection ofantineutrinos close to reactors presents several advantages: it could be performed remotely, it reflects the fuel contentand the thermal power of the reactor. The monitoring of on-load reactors as well as some of the future reactor designsis challenging for conventional safeguard techniques. In the case of on-load reactors, such as CANDU reactors orPebble Bed Modular Reactors or Molten Salt Reactors, it is not necessary to stop the operation of the core to refuelit. For these reactors, an antineutrino detector placed outside the containment walls at a moderate distance couldoffer an instrument for bulk accountancy of the fuel content of the core. To infer to which extent antineutrinos couldprovide a diversion signature, the characterization of the antineutrino source associated to different contemporaryor future reactor designs and fuels is mandatory. This is to be the first step of a feasibility study and necessitatesthe development of simulation tools [29]. The summation method is the only predictive method that could allowsuch calculations. Potential applications of antineutrino detectors at reactors were listed if this novel technology isapproved [30]. These designs imply fission induced by thermal and fast neutrons for various fuels. The fission-yielddata are still scarce for fuels deviating from the most standard ones in use in today’s power plants, and the GEFmodel can provide a means to get reliable predictions with uncertainties.In the first part of this article, after a presentation of the GEF model, we present comparisons between antineutrinoenergy spectra built with the JEFF and the GEF fission yields. We explain how it led to improvements of the modelthrough the adjunction of experimental constraints such as the LOHENGRIN sets of fission yields. We then show thelevel of agreement reached between JEFF and GEF on the antineutrino energy spectra from a standard power reactorfuel. In the second part of this article, we review the experimental methods available to bring additional experimentalconstraints to the evaluated fission yields. We then give a general view on a large variety of fissioning systems withthe aim to test the validity of the postulated regularities of the GEF model, which are crucial for its predictive power.The comparison is made for all systems, for which empirical fission-product yields from evaluations or from selectedhighly accurate kinematic experiments on thermal-neutron-induced fission are available. (In this work, evaluated dataare considered as empirical information, because they are essentially based on measured data.) In addition, the fast-5 I THE GEF MODEL neutron-induced fission of
U is included due to its contribution to the antineutrino production in a reactor. Thiswide overview that includes also many systems, which do not contribute to the antineutrino production in currentlyoperated reactors, allows us to obtain a complete picture of the deviations between GEF and the available empiricaldata and to locate their origin. It is also useful for estimating the antineutrino production in future fission reactorswith different kinds of fuel. In the last section of this article, we provide predictions of antineutrino energy spectrafor the corresponding fissioning systems.
II. THE GEF MODEL
The fully theoretical (microscopic) description of the complete fission process has not yet attained the accuracythat makes it suitable for technical applications. Only the description of pre-saddle and post-scission phenomena, inparticular the fission cross section and the de-excitation of the fission fragments, is well mastered by highly developedand rather sophisticated optical-model and by dedicated statistical de-excitation codes, respectively, while the dynam-ical evolution of the system between saddle and scission, which is decisive for the fission yields, poses still a severechallenge to theory, see [31].Therefore, we focus in this contribution on a semi-empirical approach, the general fission model GEF [28], which isbased on a number of concepts and laws of general validity. GEF has shown to reproduce measured data remarkablywell, and, thus, it is reasonable to expect its predictive power to be most reliable. GEF covers the whole fission process,starting with the formation of an excited system and ending after the radioactive decay of the fission products towardsthe beta-stable end products. This model has a set of empirical parameters, which are adjusted to the availableempirical information. The GEF model with a set of well adjusted parameters is able to predict the fission quantitiesof other systems with an accuracy comparable with the uncertainties of the experimental data used for the parameterfit [32].
A. Concept
A detailed description of the GEF model can be found in Ref. [28]. Here, we only give a succinct and somewhatsimplified description of the main ideas that are specific to the GEF model. The calculations in this work wereperformed with the version GEF-Y2019/V1.2 [33].Fig. 1 shows a flow diagram of the GEF code, which documents the treatment of the different steps of the fissionprocess.- The GEF code uses the Monte-Carlo approach to generate event-by-event information of nearly all observables.- Each event starts from a specific, possibly excited and rotating, nucleus as given by the user (spontaneous fissionfrom the nuclear ground state or by specifying the reaction, e.g. neutron or proton bombardment, or by indicatingthe compound nucleus and its excitation energy and angular momentum directly). GEF calculates the decay of thesystem by fission in competition with the emission of neutrons, protons and photons. Pre-equilibrium emission is alsoincluded whenever suited.-In case the system is committed to fission, the distributions of the fragment properties at scission ( A , Z , kineticenergies, excitation energies and deformation) are calculated. Then, the de-excitation of the primary fragments iscalculated by a competition between neutron, proton and gamma emission, till the cold secondary products reach theground state or an isomeric state. For those products which are radioactive, GEF can also compute their decay bybeta emission, delayed neutrons etc.The main ingredients of the GEF code entering the modeling of the fission probability and fragment properties, andwhich are often specific to GEF, are shortly discussed below. The modeling of particle evaporation and gamma emis-sion, in an extended Weisskopf theory with explicit consideration of angular-momentum-dependent nuclear properties,is more standard and is not mentioned further. Details can be found in [28]. a. Fission barriers: The most important physical property for the modeling of the fission probability is the fissionbarrier. The fission barriers are calculated by use of the topographic theorem [34] as the sum of the macroscopic barrierand the additional binding energy by the ground-state shell correction. This approach avoids the uncertainties of thetheoretical shell-correction energies. b. Fission channels:
Fission-fragment yields are given by the sum of the yields associated to different fission chan-nels. The fission channels are related to the statistical population of quantum oscillators in the mass-asymmetry degreeof freedom that form the fission valleys in the multidimensional potential-energy landscape. The three parameters ofthe oscillators (position, depth, and curvature) are traced back to the macroscopic potential (symmetric, ’super-long’fission channel SL) and to shells in the proton and neutron subsystems of both fragments (’standard’ fission channelsS1 and S2), which are assumed to be effective already at or little behind the outer saddle [35]. The description of the6
Concept II THE GEF MODEL
Input ofparameters(Z,A,entrance channel)and output optionsPre-equilibriumemissionandmulti-chancefission:Monte-CarlocalculationStart event loopFissioningnucleusStart MC loopCalculation of average fragment propertiesModelparameters Monte-Carlo samplingof pre-neutronfragment propertiesEmission of prompt neutronsand prompt gammas WriteoutputfilesAccumulationof pre-neutronfragment propertiesMC List of fissioningnuclei(Z, A, E*, ..)Tables of average fragmentpropertiesAccumulation of post scissionprompt gammasand neutronsAccumulation of post-neutronfragmentpropertiesEndMC loopEndevent loop Accumulationof pre-scissionparticle emissionBeta decay,delayed neutrons/gammas,cumulative yields Accumulation of beta-delayed quantities
FIG. 1. Flow chart of the GEF code.
S2 fission channel requires two additional parameters, because its shape is parametrized as a rectangular distributionconvoluted with two Gaussian distributions at the inner and the outer side, respectively.These shells are assumed to be essentially the same for all fissioning systems. Only the superposition of differentshells and the interaction with the macroscopic potential cause the different mass distributions found for differentsystems [36]. These shells also determine the shapes (mainly the quadrupole deformation) of the nascent fragments atscission. According to Strutinsky-type calculations, the fragment shapes are found to be characterized by a linearlyincreasing quadrupole deformation as a function of the number of protons, respectively neutrons, in regions betweenclosed spherical shells [37]. Also the charge polarization (deviation of the
N/Z degree of freedom at scission - meanvalue and fluctuations - from the
N/Z value of the fissioning nucleus) is treated by the corresponding quantum oscillator[38]. c. Energy sorting:
The excitation energy of the fragments at scission is essential to determine the de-excitation ofthe fragments via prompt neutron and gamma emission after scission. To infer the excitation energy of the individualfragments at scission, it is necessary to model how the total available intrinsic excitation energy at scission is sharedbetween the two fragments. In GEF, this is ruled by the so called energy-sorting process. By the influence of pairingcorrelations, the nuclear temperature below the critical pairing energy is assumed to be constant [39]. Therefore, thedi-nuclear system between saddle and scission consists of two coupled microscopic thermostates [40]. This leads to asorting process of the available intrinsic energy before scission [41, 42], where most of the excitation energy availableat scission goes to the heavy fragment. The energy sorting has an important influence on the odd-even effect in thefragment Z distribution [43] and on the fragment-mass-dependent prompt-neutron multiplicity [40].7 Concept III GEF IMPROVEMENTS USING REACTOR ANTINEUTRINOS AND APPLICATION TOANTINEUTRINO PRODUCTION
B. Strengths and weaknesses
The GEF model combines a well defined theoretical framework of basic concepts and laws of general validity with theability to closely reproduce measured fission observables by adjusting the values of the model parameters in a ratherdirect and flexible way. Thus, it goes well beyond the purely empirical description of systematics without the necessityof a complete and accurate quantitative understanding of the physics in an ab-initio approach. The concept of theGEF model combines the strength of empirical systematics with the strength of a rather far-reaching understandingof the physics. This leads to a good reproduction of measurements and a good predictive power [28, 31, 32]. On theother hand, a good description of a specific feature is only possible, if the relevant experimental data for determingthe corresponding GEF parameters are available.
III. GEF IMPROVEMENTS USING REACTOR ANTINEUTRINOS AND APPLICATION TOANTINEUTRINO PRODUCTION
Antineutrino energy spectra of individual fission products obtained from nuclear databases have been used to refinethe GEF code in order to improve its potential of predictiveness for reactor antineutrinos. In the present section,reactor antineutrino energy spectra have been computed using summation calculations with decay data taken fromnuclear databases and fission yields taken respectively from JEFF-3.1.1, JEFF-3.3 and GEF. The direct comparisonof the three calculations allowed us extensively improving the predictions of GEF for antineutrinos by acting on a fewwell identified parameters, depending on the fission channel concerned.
A. Summation calculations for antineutrinos
The summation method is based on the use of nuclear data combined in a sum of all the individual contributions ofthe beta branches of the fission products, weighted by the amount of the latter nuclei. Two types of datasets are thusinvolved in the calculation: fission yields and fission-product decay data. This method was originally developed by [44]followed by [45] and then by [46, 47]. The β /¯ ν spectrum per fission of a fissionable nuclide S k ( E ) can be broken-upinto the sum of all fission products β /¯ ν spectra weighted by their activity A fp S k ( E ) = N fp (cid:88) fp =1 A fp × S fp ( E ) (1)Eventually, the β /¯ ν spectrum of one fission product is the sum over N B beta branches (b) of all beta-decay spectra(or associated antineutrino spectra), S bfp (in eq 2), of the parent nucleus to the daughter nucleus weighted by theirrespective branching ratios ( BR bfp ) as S fp ( E ) = N B (cid:88) b =1 BR bfp × S bfp ( Z fp , A fp , E b fp , E ) (2) E b fp being the endpoint of the b th branch of a given fission product.In the summation spectra presented in this article, the beta-decay properties of the fission products have beenselected following the prescription of [23] and include the most recent Total Absorption Gamma-ray Spectroscopy(TAGS) data which are free from the Pandemonium effect [48]. The Pandemonium effect is the main bias of theantineutrino energy spectra computed with the summation method, its impact being larger than other nuclear effectssuch as forbidden non-unique shape factors or the weak magnetism correction. It arises from the use of germaniumdetectors to detect the beta branches of beta decays with large Q-value. In some cases, the lack of efficiency of thesedetectors to high energy or multiple gamma-rays induce the misdetection of beta branches towards high energy statesin the daughter nucleus. This leads to the distortion of the beta and antineutrino spectra with an overestimate of thehigh energy part. The measurement of beta-decay properties with the TAGS technique [49] allows circumventing theproblem, and experimental campaigns focused on nuclei contributing importantly to the reactor antineutrino spectrahave been performed in Jyv¨askyl¨a since 2009 [20, 21, 50–53], leading to an impressive improvement of the agreementbetween the summation method predictions and the Daya Bay experimental results [23].8 Parameter valuesIII GEF IMPROVEMENTS USING REACTOR ANTINEUTRINOS AND APPLICATION TOANTINEUTRINO PRODUCTION
FIG. 2. Ratio of the antineutrino spectra GEF/JEFF-3.1.1 before the tuning (blue line) using antineutrino energy spectra andadditional fission-yield data and after (red line).
B. Sensitivity of antineutrino spectra to the fission yields
Figure 2 (dashed line) shows the level of agreement that was reached between the antineutrino spectra of the GEFpredictions and those obtained with the JEFF-3.1.1 fission yields with a previous version of GEF (GEF-Y2017/V1.2)that was in good agreement with the integral data of the decay heat after fission pulses of various fissioning systems[31]. The antineutrino energy spectra of
U and
Pu computed with the two sets of fission yields were in agreementonly at the 10-30% level even in a restricted energy range up to 6 MeV. Though this previous version of GEF alreadyprovided very good reproduction of decay heat after thermal fission pulses for
U and
Pu, it was not satisfactoryto meet the additional exigence of the dependence in energy of the antineutrino spectra. The adjustment of the GEFmodel documented in [28] had been performed with a general fit to all mass yields from ENDF/B-VII.0, because thisevaluation provided the widest coverage of fissioning nuclei [54].This way, data of very different quality, including faulty data, which spoiled the quality of the result, were includedin the fit on the same footing, see section VI B. This may explain why the antineutrino spectra obtained with thefission yields of the previous version of GEF deviate so strongly from those obtained with the yields from the morerecent JEFF-3.1.1 evaluation.The extraction of the list of nuclei contributing importantly to the antineutrino energy spectra (lists commentedin section VII) has allowed to evidence the causes of the discrepancies between GEF and experimental fission yieldsfor these nuclei. The antineutrino spectra are particularly sensitive to the yields of specific nuclides, especially at thehigher antineutrino energies. In addition, the relatively large uncertainties of JEFF-3.1.1 and JEFF-3.3 fission yieldssuggested a good reproduction by the GEF model with rather large deviations. Deviations inside the error bars of theevaluations lead to substantial variations in the antineutrino spectrum. These remaining discrepancies had only littleimpact on other observables such as the decay heat after fission pulses but showed to impact a lot the antineutrinospectra. Additional experimental constraints on fission yields were needed, and this conclusion triggered the use of theLOHENGRIN data which eventually allowed to improve the predictiveness of the model because they are much moreaccurate, as shown in the sections V and VI of this article. The reactor antineutrino observable is thus a stringentadditional constraint for the evaluation of nuclear data, and its combination with the GEF model allows to tackle thesource of remaining inconcistencies in the data. It is important to underline here that the GEF parameters have beentuned globally so that these results constrain also all the other predictions for different fissioning systems.The solid lines in Fig. 2 illustrate the improvement achieved after the tuning with GEF-Y2019/V1.2 using thereactor antineutrino observable as explained above. It is more extensively quantified in section VII where useful resultsassociated to reactor antineutrino of interest for the fission process and for reactor surveillance are also presented. Thelevel of accuracy reached for the mass yields between GEF and the evaluated data and the experiments is presentedand discussed in the section VI. Comparisons of independent yields from JEFF-3.3 and GEF are shown in AppendixI.
C. Parameter values
The study performed on the fission yields led to the introduction of a few modifications of the GEF parameters tobetter represent the empirical fission yields of the JEFF-3.1.1 and the JEFF-3.3 evaluations as well as the LOHENGRINexperiments (comparison provided in section VI), which were not considered before using antineutrino summationcalculations as explained above. In particular, the very accurate mass yields of the LOHENGRIN experiments required9
Parameter values IV EXPERIMENTAL APPROACHES an individual adjustment of some GEF parameters, depending on the Z value of the fissioning nucleus. Still, all isotopesof a given element are described with the same parameter set. The parameter values of GEF-Y2019/V1.2 are veryclose to the ones documented in Ref. [32]. The modified parameter values (all related to the modeling of the fissionchannels) are documented in Table I.The strength of the shell effect for symmetric fission has to be determined for individual fissioning systems, becausethe nuclides formed in symmetric fission depend on the composition of the fissioning nucleus. However, this was onlypossible in a limited number of cases, where the required experimental information is available. These values are listedin Table II. They vary by a few 100 keV. Such a small difference underlines the high sensitivity of the fragment yieldat symmetry to this critical parameter. TABLE I. List of locally adjusted parameter values.Global values Locally adjusted valuesParameter Z = 90 Z = 93 , , P_DZ_Mean_S1
P_DZ_Mean_S2
P_Shell_S2 -4.4 MeV -4.8 MeV (-4.4 MeV)
P_Z_Curv_S2
S2leftmod
P_A_Width_S2 Z different from 90, 93, 94, and 95. The parameter names are defined as: • P_DZ_Mean_S1 : Shift of the S1 fission channel in Z with respect to the global value. • P_DZ_Mean_S2 : Shift of the S2 fission channel in Z . • P_Shell_S2 : Strength of the shell behind the S2 fission channel. • P_Z_Curv_S2 : This parameter determines the smoothing of the inner side of the potential pocket of the S2 fissionchannel. • S2leftmod : This parameter determines the smoothing of the outer side of the potential pocket of the S2 fissionchannel. • P_A_width : Flat part of the S2 potential pocket.For a detailed explanation of these parameters, see also [28, 32].In the next section we will detail the existing experimental approaches used to constitute the pool of availablefission-yield data and provide their strengths and weaknesses. Then we illustrate how the yields of the tuned versionof GEF eventually compare to experiments.
IV. EXPERIMENTAL APPROACHES
The fission process ends up in two fission products, which populate about a thousand different nuclides. (We donot consider ternary fission here, where a third light particle is formed, in addition, with low probability.) Severalexperimental approaches have been developed for measuring the yields of the different fission products formed in thefission of a specific nucleus at a certain excitation energy and angular momentum. We will consider some of those,which are most often used. See Ref. [58] for an extensive overview on presently used experimental approaches infission. 10
Radiochemistry IV EXPERIMENTAL APPROACHES
TABLE II. Adapted values of the strength of the shell effect for symmetric fission. Z = 89 A = 226 Delta_S0 /MeV = -0.3 Z = 90 A = 228 229 230 231 232 233 Delta_S0 /MeV = 0.2 0.4 0.7 0.8 0.9 0.9 Z = 92 A = 233 234 allother Delta_S0 /MeV = 0.4 0.4 0.2 Z ≥ A = all Delta_S0 /MeV = -0.3Note: The values are adjusted to the relative yield of the symmetric channel in measured mass distributions. Data fromJEFF-3.3 (n th ,f) and refs. [56, 57] (transfer reactions) were used. For all other cases: Delta_S0 = 0. See refs. [28, 32] for theexact meaning of
Delta_S0 . A. Radiochemistry
1. The method
The traditional method for measuring fission-product yields consists of exposing samples to a flux of neutrons. Afterirradiation, the samples are investigated by gamma spectroscopy [59]. The fission products are identified unambigu-ously in Z and A by measuring the gammas emitted directly or in their radioactive decay chain, and their yields arededuced from the intensities of the gamma lines. Chemical separation is often applied in order to purify the gammaspectra by reducing the background radiation.
2. Independent and cumulative yields
The primary fission fragments, as they are formed at scission, normally carry some excitation energy that givesrise to a cascade of prompt neutrons and prompt gammas, until the ground state or a longer-lived isomeric state isreached. (Processes are called to be prompt, if they occur inside a certain time window that is much shorter thantypical beta-decay half-lifes, which are in the milli-second range or longer.) The yields of the fission products formedright after the prompt processes are called independent yields.Only the gamma radiation emitted in a time range starting a few seconds (or longer) after fission, which is neededfor the extraction of the target and, possibly, the chemical separation, can be measured by radiochemistry. Therefore,the yields of the most neutron-rich fission products, which are especially short-lived, cannot be determined directly.The yields including also the products of the consecutive radioactive decay are called cumulative yields. Becausebeta-delayed neutron emission, which changes the nuclear mass number, is a rare process, the last cumulative yieldsnear the beta stability are a rather good measure of the mass yields. However, the application of the summationmethod for estimating the antineutrino production is based on the independent yields, which requires the additionalknowledge of the fission-product atomic number before beta decay.
3. Yields of short-lived products
Methods have been developed to determine even the independent yields of short-lived radioactive fission products,fully identified in Z and A , by requiring consistency between the neutron-deficient wing of the nuclide distributionin the light fission product and the neutron-rich wing of the nuclide distribution in the heavy product (and viceversa) with the mass-dependent multiplicity of prompt neutrons [60]. The application of this method on the basisof incomplete or even fragmentary experimental data requires a good knowledge of the behavior of fission-fragmentnuclide distributions and prompt-neutron multiplicities. One of the most popular systematics used for this purposewas developed by Wahl [61]. 11 Experiments with particle detectors in direct kinematics IV EXPERIMENTAL APPROACHES
4. Strengths and weaknesses
The main strength of the radiochemical method is the unambiguous identification of the fission products in Z and A . Also the sensitivity down to very low yields (10 − % or lower [62]) is a strength of this method.However, there are several weaknesses of this method: Due to the time delay between irradiation and measurement,this method is slower than the lifetimes of many fission products, in particular of the most neutron-rich ones. Therefore,the independent yields of short-lived fission products cannot directly be measured, and their indirect determination(see above) depends on certain assumptions.Another weakness is the uncertainty introduced by the spectroscopic information that is used to infer the number offission products from the intensities of the gamma lines. Misidentification of a gamma line can also lead to erroneousresults. Moreover, target impurities may be an issue, regardless of the measurement method.The application of this method is limited to suitable targets and available neutron sources with suitable energies.Most of the available data were obtained with thermal neutrons, ”fast” neutrons with energies around 1 MeV that areproduced in the evaporation process, possibly partly moderated, and with 14-MeV neutrons. B. Experiments with particle detectors in direct kinematics
1. The method
Instead of exploiting the radioactivity of the fission products with the radiochemical method, their high kineticenergies have been used to detect and identify the fission products by their ionization signals in different kind ofdetectors. This way, the energy loss in thin detectors, the total energy in thick detectors, and/or the time-of-flightbetween two detectors were measured, eventually those of both fission products simultaneously. However, in mostcases the additional measurement of the deflection in the electric and/or magnetic field in powerful spectrometerswas used to determine the yields of individual nuclides with sufficient resolution in Z and A . We consider here theLOHENGRIN spectrometer [63], where the full mass distribution and the Z distribution in the lighter fission productwere measured for the thermal-neutron-induced fission of a number of systems.
2. Strengths and weaknesses
A great advantage of kinematic measurements at the LOHENGRIN spectrometer is the rather direct determinationof fission-product yields by ion counting with 100% detection efficiency for ions that reach the detector. Nevertheless,a few corrections must be applied in order to account for the burn-up of the target material and the deterioration of thetarget quality by diffusion of the target material into the backing [64]. Furthermore, the fission products appear witha distribution of ionic charge states. These distributions have to be measured separately, and the associated yieldshave to be added up. A peculiar difficulty consists in the shift of the ionic charge-state distribution due to internalconversion and a consecutive Auger cascade for specific nuclides [65]. These cannot be calculated with sufficientaccuracy and must be determined experimentally by a scan over the charge-state distribution of all fission products.Therefore, a good quality of the data requires a very careful analysis and correction of these disturbing effects.In addition to the limitation to thermal-neutron-induced fission of a few suitable target nuclei, the kinetic-energydistribution of the fission products cannot be covered completely by practical reasons. The full distribution must beestimated from the measurements at a few kinetic-energy values. This may introduce some systematic uncertainties.Mass yields can be measured over the whole fission-product range. However, we mention that kinematic mea-surements of independent fission-product yields, fully determined in A and Z , can only be performed for the lighterproducts. A combination of mass separation by the LOHENGRIN spectrometer and full nuclide identification bygamma spectroscopy, which has recently been introduced [66] but not yet used in the evaluations, is applicable alsofor the heavy fission products, but it depends again on the uncertainties of the gamma detection and the necessarygamma-spectroscopic information. 12 Overall impression VI COMPARATIVE STUDY
C. Experiments with particle detectors in inverse kinematics
1. The method
During the last years, an innovative experimental approach based on the use of inverse kinematics has been intro-duced [67–70]: The fissioning nucleus is prepared with high kinetic energies, and, thus, the fission products are emittedwith velocities that are appreciably higher than those, which they get in the fission process in direct kinematics.
2. Strengths and weaknesses
Excellent resolution in A and Z has been obtained, but, partly due to the insufficiently well defined initial excitationenergy of the fissioning system, the results have not yet been exploited so much for extracting nuclear data for technicalapplications. Therefore, we mention this method only for completeness and for its growing importance in the future,but we will not consider this method here further. We would like to mention that the GEF model could help to betterinterpret the measured data by providing an estimation of the energy dependence of the fission yields. An applicationof this method is used in section VI A 2 for the modeling of the mass yields of fast-neutron-induced fission of U. V. EVALUATIONS
Evaluation assesses the measured data and their uncertainties, reconciles discrepant experimental data and fillsin missing data by exploiting systematic trends of the measured data in order to provide reliable nuclear data,primarily for applications in nuclear technology. Evaluation work is organized, and the resulting nuclear-data tablesare disseminated by several nuclear-data centers under the auspices of the International Atomic Energy Agency.In the following, we will consider the evaluations ENDF/B-VII, JEFF-3.1.1 and JEFF-3.3. (Note that all fission-fragment yields used in this work have identical values in ENDF/B-VI.8, ENDF/B-VII.0, ENDF/B-VII.1, andENDF/B-VIII.0 [54].) The main sources of these evaluations are data from radiochemical measurements, supplementedby only a few data from LOHENGRIN experiments, in spite of their special advantages in accuracy. Theoretical fissionmodels have been exploited only very little up to now.
VI. COMPARATIVE STUDY
Although the characteristics of the antineutrino emission in fission is specific to the fission-product nuclide, deter-mined in Z and A , it is meaningful, as a first step, to assure a good description of the mass yields, because theseare usually measured with the highest accuracy. In the present section, we compare the fission-product mass distri-butions for thermal-neutron-induced fission of all systems, which are included in the ENDF/B-VII, the JEFF-3.1.1or the JEFF-3.3 evaluation or for which experimental data from LOHENGRIN experiments are available, with theresult of GEF-Y2019/V1.2. In addition, fast-neutron-induced fission of U is included. For a quick overview of theessential results, important conclusions and recommendations are given in italic. Throughout the paper we will usethe following notations: n th means thermal neutrons, n fast means fast neutrons, and n hi means neutrons of 14 MeV.A systematic comparison of the independent yields of fully identified nuclides of the four systems U(n th ,f), U(n fast ,f),
Pu(n th ,f), and Pu(n th ,f) from GEF and from JEFF-3.3 is presented in Appendix I. A. Overall impression
In the present subsection VI A, the mass yields from the GEF code are compared with evaluated data or resultsfrom LOHENGRIN experiments, where at least satisfactory agreement has been obtained. At the same time, theseare the systems that have been experimentally investigated the most intensively, and the data are expected to be themost reliable. Cases with larger deviations are discussed in section VI B. We concentrate here mostly on thermal-neutron-induced and fast-neutron-induced fission. A more general overview was given in Ref. [28], however with anolder version of the GEF code. 13
Overall impression VI COMPARATIVE STUDY
1. Illustrative cases
FIG. 3. Mass yields of
Th(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with ENDF/B-VII (black symbols with error bars). Here and in the following figures, the green lines show thecontributions of the different fission channels from GEF.FIG. 4. Mass yields of Th(n th ,f), linear (upper frame) and logarithmic (lower frame) scale, GEF result (red points) incomparison with the data of a LOHENGRIN experiment (blue symbols). a. Mass yields of Th(n th ,f ): Figs. 3 and 4 show comparisons of the mass yields from GEF with the data fromthe ENDF/B-VII evaluation and from a LOHENGRIN experiment [71] for the system
Th(n th ,f). There is fairagreement, except some underestimated intensities of the peaks near A = 85 and A = 144, which becomes significantin comparison with the LOHENGRIN data due to their appreciably higher accuracy. These deviations hint to a14 Overall impression VI COMPARATIVE STUDY problem in the description of the S2 fission channel in GEF . This problem might be cured by the introduction of amore complex shape of the S2 contribution to the mass yields. However, this is beyond the scope of the present statusof GEF, because a higher degree of complexity and the corresponding introduction of additional model parametersmight endanger the predictive power of the model. The symmetric yield is slightly overestimated. b. Mass yields of
U(n th ,f ): Figs. 5, 6, 7, and 8 show comparisons of the mass yields from GEF with thedata from the ENDF/B-VII, JEFF-3.1.1 and JEFF-3.3 evaluations, as well as from a LOHENGRIN experiment [72]for the system
U(n th ,f). There is fair agreement. However, the yields near A = 90 and A = 136 are somewhatunderestimated, while the yields near A = 98 are somewhat overestimated. Again, this is most significant in comparisonwith the LOHENGRIN data. These discrepancies appear with respect to the data from all sources. Thus, they mustprobably be attributed to deficiencies of GEF , probably due to restrictions in the shape of the mass distribution of theasymmetric fission channel S2. This is in line with the observations for the system
Th(n th ,f).15 Overall impression VI COMPARATIVE STUDY
FIG. 5. Mass yields of
U(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with ENDF/B-VII (black symbols).FIG. 6. Mass yields of U(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.1.1 (black symbols). In addition, the yields in the inner wings of the asymmetric peaks are somewhat underestimated. In view of thegood agreement between GEF and the evaluations in this mass region for the especially carefully studied system
U(n th ,f), a common deficiency of all these evaluations for U(n th ,f) due to some erroneous experimental data maybe assumed. A bump near A=124 in ENDF/B-VII does not appear in the JEFF evaluations anymore. In spite ofdifferences between the evaluations, the yield at symmetry seems to be slightly overestimated. In addition, its shapeis concave, while evaluations suggest a more flat, or even convex, pattern. c. Mass yields of U(n th ,f ): Figs. 9, 10, 11, and 12 show comparisons of the mass yields from GEF with thedata from the ENDF/B-VII, JEFF-3.1.1 and JEFF-3.3 evaluations, as well as from LOHENGRIN experiments [73, 74]16
Overall impression VI COMPARATIVE STUDY
FIG. 7. Mass yields of
U(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.3 (black symbols).FIG. 8. Mass yields of U(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with LOHENGRIN data (blue symbols). for the system U(n th ,f), which is the most intensively studied and best known system of all.The data of all evaluations are rather well reproduced. Deviations rarely exceed the uncertainties of the evaluations.The clearest picture is provided by the comparison with the LOHENGRIN data, which have by far the smallestuncertainties. Here some deviations appear in slightly underestimated yields around A = 90 and slightly overestimatedyields around A = 94, which again hints to some shortcoming in the shape of the S2 fission channel in GEF . Theevaluations show similar deviations, but only the error bars of the ENDF evaluation are small enough in this massregion to make these significant. Moreover, some yields of the extremely asymmetric splits are overestimated, wherethe super-asymmetric fission channel dominates. We note that the yield at symmetry is very slightly overestimated.17 Overall impression VI COMPARATIVE STUDY
FIG. 9. Mass yields of
U(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with ENDF/B-VII (black symbols).FIG. 10. Mass yields of U(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.1.1 (black symbols). d. Mass yields of Np(n th ,f ): Figs. 13, 14, and 15 show comparisons of the mass yields from GEF with thedata from the JEFF-3.1.1 and JEFF-3.3 evaluations, as well as from LOHENGRIN experiments [75, 76] for the system
Np(n th ,f) (by the Np(2n th ) reaction). Again, the LOHENGRIN data have the smallest uncertainties. The dataare quite well reproduced. Some deviations are found in the inner wings of the asymmetric peaks with JEFF-3.1.1,while there is good agreement with JEFF-3.3. The shape of the distribution near symmetry of JEFF-3.1.1 shows asharp minimum, while JEFF-3.3 and GEF show a plateau-like shape, however at different levels. The LOHENGRINdata do not reach above A =100. However, they show a slight underestimation of GEF near A =96. The yield atsymmetry is overestimated. 18 Overall impression VI COMPARATIVE STUDY
FIG. 11. Mass yields of
U(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.3 (black symbols).FIG. 12. Mass yields of U(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with LOHENGRIN data (blue symbols). e. Mass yields of Pu(n th ,f ): In Figs. 16 and 17, the mass yields from GEF are compared with the data fromthe JEFF-3.1.1 and the JEFF-3.3 evaluations for the system
Pu(n th ,f).19 Overall impression VI COMPARATIVE STUDY
FIG. 13. Mass yields of
Np(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.1.1 (black symbols).FIG. 14. Mass yields of Np(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.3 (black symbols). Overall impression VI COMPARATIVE STUDY
FIG. 15. Mass yields of
Np(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with data from a LOHENGRIN experiment (blue symbols). Overall impression VI COMPARATIVE STUDY
FIG. 16. Mass yields of
Pu(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.1.1 (black symbols). We note the reasonable description (height and shape) of the symmetric yield. In the two peak regions, there aresome deviations seen between both evaluations and GEF in linear scale: In GEF, the peaks are shifted to largerasymmetries. These deviations are astonishing, because the mass yields of the neighboring system
Pu(n th ,f) arevery well reproduced (see below). In the shoulders of the asymmetric peaks, there are systematic deviations seen inlogarithmic scale: While GEF reproduces well the outer wings of JEFF-3.1.1 and the inner wings of JEFF-3.3, there aresystematic shifts on the inner wings of JEFF-3.1.1 and the outer wings of JEFF-3.3. A simultaneous reproduction ofthe mass yields of Pu(n th ,f) and Pu(n th ,f) from both JEFF-3.1.1 and JEFF-3.3 is in conflict with the regularitiesimposed by the physics of GEF. Considering in addition the rather limited data base for Pu(n th ,f) that was availablefor the evaluations, we tentatively recommend to use the GEF mass yields .Finally, we would like to mention that Pu is a thermally not-fissile nucleus. Therefore, the fission-product yieldsmeasured in a pressurized-water reactor (PWR) originate to 42.1% from neutrons with energies above 400 keV [80].The expected enhancement of the evaluated yields at symmetry seems to be too weak to be seen. f. Mass yields of
Pu(n th ,f ): Figs. 18, 19, 20, and 21 show comparisons of the mass yields from GEF withthe data from the ENDF/B-VII, JEFF-3.1.1 and JEFF-3.3 evaluations, as well as from a LOHENGRIN experiment[77] for the system
Pu(n th ,f). The data of all evaluations are rather well reproduced. The smallest deviations arefound with respect to the LOHENGRIN data, which have by far the smallest uncertainties. We would like to drawthe attention to an interesting detail: In the LOHENGRIN data there appears a clear shoulder at A = 84, dominatedby Se, which is well reproduced by GEF. According to GEF, this shoulder marks the transition from the S2 tothe super-asymmetric fission channel. This shoulder does not appear in the evaluations. This shoulder is seen, lesspronounced, also in the GEF results for
Pu(n th ,f). We note the good description around symmetry, namely whencompared to ENDF/B-VII. g. Mass yields of Pu(n th ,f ): Fig. 22 shows the comparison of the mass yields from GEF with the data fromthe ENDF/B-VII evaluation for the system
Pu(n th ,f). The data are rather well reproduced, except near symmetry,where the yields from GEF are lower. This may be explained by the fact that Pu is a thermally not-fissile nucleus,like
Pu, which was discussed before. The evaluation shows an unexpected asymmetry in this region, which is notpresent in the ENDF/B-VII and the JEFF-3.3 evaluations of the more intensively investigated system
Pu(n th ,f).The GEF yields of the most asymmetric masses are slightly below the evaluation. h. Mass yields of Pu(n th ,f ): Fig. 23 shows the comparison of the mass yields from GEF with the data fromthe ENDF/B-VII for the system
Pu(n th ,f). The data are rather well reproduced, except near symmetry and for A around 160, where the yields from GEF are lower. The underestimation of the mass yields at symmetry may again beexplained by the fact the Pu is a thermally not-fissile nucleus, like
Pu and
Pu. Again, there is an unexpectedasymmetry around the symmetric valley in the evaluation.22
Overall impression VI COMPARATIVE STUDY
FIG. 17. Mass yields of
Pu(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.3 (black symbols).FIG. 18. Mass yields of Pu(n th ,f), linear (upper frame) and logarithmic (lower frame) scale, GEF result (red points) incomparison with ENDF/B-VII (black symbols). Overall impression VI COMPARATIVE STUDY
FIG. 19. Mass yields of
Pu(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.1.1 (black symbols).FIG. 20. Mass yields of Pu(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.3 (black symbols). Overall impression VI COMPARATIVE STUDY
FIG. 21. Mass yields of
Pu(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with data from a LOHENGRIN experiment (blue symbols). Overall impression VI COMPARATIVE STUDY
FIG. 22. Mass yields of
Pu(n th ,f), linear scale (upper frame) and logarithmic (lower scale), GEF result (red points) incomparison with ENDF/B-VII (black symbols).FIG. 23. Mass yields of Pu(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with ENDF/B-VII (black symbols). i. Mass yields of Am(n th ,f ): Figs. 24, 25, and 26 show the comparison of the mass yields from GEF with thedata from ENDF/B-VII, JEFF-3.1.1 and JEFF-3.3 for the system
Am(n th ,f). The data are rather well reproduced.Fission of Am in a PWR include a fraction of 65.4% induced by neutrons with energies above 400 kV [80],which could explain why the mass yields around symmetry from ENDF/B-VII and JEFF-3.3 are underestimated byGEF. Some more deviations appear in the upper wing of the distribution above A = 155: The yields from GEF aresystematically lower than the values from ENDF/B-VII and JEFF-3.1.1 and, to a lesser extent from JEFF-3.3, whilethere is rather good agreement in the lower wing of the distribution below A = 82. It is not obvious to attribute thedeviations in the upper wing to deficiencies of GEF , because physics connects the yields in the two outer wings with26
Overall impression VI COMPARATIVE STUDY
FIG. 24. Mass yields of
Am(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with ENDF/B-VII (black symbols).FIG. 25. Mass yields of Am(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.1.1 (black symbols). the mass-dependent prompt-neutron multiplicities: A shift in the upper wing to higher masses with respect to GEF,while keeping the lower wing unchanged, as suggested by the evaluations for Am(n th ,f) demands a reduction ofthe prompt-neutron yields in the heavy-mass region with respect to the systematics of other systems, for example Pu(n th ,f), where the mass yields from GEF agree with the empirical data over the whole mass range. j. Mass yields of m Am(n th ,f ): Figs. 27 and 28 show the comparison of the mass yields from GEF with thedata from ENDF/B-VII and JEFF-3.1.1 for the system m Am(n th ,f). The data of the evaluations are rather wellreproduced by GEF with slightly underestimated yields at symmetry in the case of JEFF-3.1.1.27 Overall impression VI COMPARATIVE STUDY
FIG. 26. Mass yields of
Am(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.3 (black symbols).FIG. 27. Mass yields of Am(n th ,f), linear (upper frame) and logarithmic (lower frame) scale, GEF result (red points) incomparison with ENDF/B-VII (black symbols). k. Mass yields of Am(n th ,f ): Figs. 29 and 30 show the comparison of the mass yields from GEF with the datafrom JEFF-3.1.1 and JEFF-3.3 for the system
Am(n th ,f). There are discrepancies between the GEF results andJEFF-3.1.1 near symmetry and JEFF-3.3 in the outer wings, while GEF agrees well with JEFF-3.3 near symmetryand with JEFF-3.1.1 in the outer wings, which is a rather ambiguous result that calls for clarification . l. Mass yields of Cm(n th ,f ): Figs. 31, 32 and 33 show the comparison of the mass yields from GEF withthe data from ENDF/B-VII, JEFF-3.1.1 and JEFF-3.3 for the system
Cm(n th ,f). The empirical distributions arefairly well reproduced. There are some deviations, in particular around the peaks, but it is difficult to deduce asystematic trend due to the large scattering of the evaluated yields between neighboring masses and between the28 Overall impression VI COMPARATIVE STUDY
FIG. 28. Mass yields of
Am(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.1.1 (black symbols).FIG. 29. Mass yields of Am(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.1.1 (black symbols). different evaluations, and due to their large uncertainties. m. Mass yields of Cm(n th ,f ): Figs. 34 and 35 show the comparison of the mass yields from GEF with thedata from JEFF-3.1.1 and JEFF-3.3 for the system
Cm(n th ,f). There are large deviations between the yields fromJEFF-3.1.1 and the GEF results, namely at symmetry, but the discrepancies are appreciably reduced between theGEF yields and those of the more recent JEFF-3.3 evaluation. n. Mass yields of Cm(n th ,f ): Figs. 36, 37 and 38 show the comparison of the mass yields from GEF withthe data from ENDF/B-VII, JEFF-3.1.1 and JEFF-3.3 for the system
Cm(n th ,f). The evaluated distributions arefairly well reproduced. There are some deviations between GEF and the one or the other evaluation, but they are not29 Overall impression VI COMPARATIVE STUDY
FIG. 30. Mass yields of
Am(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.3 (black symbols).FIG. 31. Mass yields of Cm(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with ENDF/B-VII (black symbols). systematical, except that the two mass peaks from GEF are less sharp. Best agreement is found between GEF andthe most recent JEFF-3.3 evaluation. o. Mass yields of Cf(n th ,f ): The fission-product mass distributions of the system
Cf(n th ,f) from bothENDF/B-VII and from a LOHENGRIN experiment are rather well reproduced by GEF, see Figs. 39 and 40. One canobserve a slight underestimation for the lightest masses in both figures. The LOHENGRIN experiment, which coversonly the light part, has provided data with very small uncertainties. Therefore, these data represent an especiallystringent test case. There is a remarkably good agreement of the GEF result with the mass yields around the lightpeak, except the yield for A=109, which is somewhat underestimated in the calculation.30 Overall impression VI COMPARATIVE STUDY
FIG. 32. Mass yields of
Cm(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.1.1 (black symbols).FIG. 33. Mass yields of Cm(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.3 (black symbols). Overall impression VI COMPARATIVE STUDY
FIG. 34. Mass yields of
Cm(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.1.1 (black symbols).FIG. 35. Mass yields of Cm(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.3 (black symbols). Overall impression VI COMPARATIVE STUDY
FIG. 36. Mass yields of
Cm(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with ENDF/B-VII (black symbols).FIG. 37. Mass yields of Cm(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.1.1 (black symbols). Overall impression VI COMPARATIVE STUDY
FIG. 38. Mass yields of
Cm(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.3 (black symbols).FIG. 39. Mass yields of Cf(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with ENDF/B-VII (black symbols). Overall impression VI COMPARATIVE STUDY
FIG. 40. Mass yields of
Cf(n th ,f), linear (upper frame) and logarithmic (lower frame) scale, GEF result (red points) incomparison with the result from an experiment [78, 79] at LOHENGRIN (blue symbols). Overall impression VI COMPARATIVE STUDY
2. Treatment of energy distributions: the case of
U(n fast ,f)
In some cases, the initial excitation energy of the fissioning nucleus extends over a range where the variation of thefission-product yields as a function of excitation energy cannot be neglected. A realistic description of the dependenceof the fission process on the initial excitation energy is mandatory for obtaining reliable results. In these cases, a seriesof theoretical calculations with a sequence of excitation energies must be performed, and the results must be addedup with the appropriate weights.In the following, we present the fast-neutron-induced fission of
U as an example for illustrating the proceduralmethod. Note that also the other nuclei ( U, , Pu) that are considered in this work for the production ofantineutrinos in a reactor are exposed to neutrons in a rather broad energy range. However, due to the large fissioncross section of these fissile nuclei at low neutron energies, the fission yields are well represented by assuming thermal-neutron-induced fission.The following data with a sharp initial excitation energy were used to benchmark the excitation energy dependenceof the fission yields in GEF: The mass yields of
U(n th ,f), shown above, and U(n,f) with E n = 14 MeV, shown inFigs. 41 and 42 from the ENDF/B-VII and the JEFF-3.3 evaluation, respectively, document well the variation of thefission yields from thermal energies to 14 MeV. In addition, the mass yields of U(n,f) with E n = 14 MeV, shown inFigs. 43 to 45 were used.One can observe a rather good agreement between the evaluated mass yields and the GEF results at fixed E n . Thegrowth of the symmetric channel with increasing energy, as well as the shift towards symmetry and the broadeningof the asymmetric modes are well reproduced by GEF. The constraints of the theoretical framework do not allow toreproduce the data exactly, and some minor deviations can be observed. Moreover, also the evaluations do not agreewith each other. In U(n,f) with E n = 14 MeV, GEF seems to slightly overestimate the yield of the symmetricmode, and its shape is not exactly reproduced. On the empirical side, in the mass yields of JEFF-3.3, there appearseveral apparently erratic deviations (at A = 112, A = 129, and A = 148 for U(n,f) and around A = 76, at A =85, A = 102, A = 116, and A = 117 for U(n,f)) from the smooth behavior of the ENDF evaluation and of GEF,which are probably not realistic. For
U(n,f) at the same neutron energy, GEF agrees with ENDF/B-VII, while theJEFF evaluations show an unexpected asymmetry near the symmetric valley. In summary, it often seems to be verydifficult to decide whether one or the other evaluation or the GEF result provides the more reliable value for a specificmass yield in a specific case.
FIG. 41. Mass yields of
U(n,f), E n = 14 MeV, linear (upper frame) and logarithmic (lower frame) scale. GEF result (redpoints) in comparison with ENDF/B-VII (black symbols). The GEF calculation of the mass yields for the system
U(n fast ,f) was performed with the distribution of initialneutron energies that lead to fission, taken from an estimation in Ref. [80]. It is the spectrum of partly moderatedfission neutrons in a PWR, multiplied with the corresponding fission cross section. The corresponding initial excitation36
Overall impression VI COMPARATIVE STUDY
FIG. 42. Mass yields of
U(n,f), E n = 14 MeV, linear (upper frame) and logarithmic (lower frame) scale. GEF result (redpoints) in comparison with JEFF-3.3 (black symbols).FIG. 43. Mass yields of U(n,f), E n = 14 MeV, linear (upper frame) and logarithmic (lower frame) scale. GEF result (redpoints) in comparison with ENDF/B-VII (black symbols). energies are shown in figure 46.The result of the calculation for the mass yields of U(n fast ,f) is compared with different evaluations in figures47, 48, and 49. The yields of the different evaluations are rather well reproduced by the GEF calculation. (Thediscrepancies between the PROFIL experiment and GEF, reported in [81], do not appear anymore with the latestGEF version due to the new adjustment of the model parameters in GEF Y2019/V1.2.) There is some overestimationof the yields below 0.1% in the low-mass tail of the distribution, where the super-asymmetric fission channel contributesappreciably, while the complementary high-mass tail is well reproduced. The low mass yields around symmetry fromGEF agree well with the ENDF evaluation, while the JEFF evaluations show an unexpectedly strong slope.37
Overall impression VI COMPARATIVE STUDY
FIG. 44. Mass yields of
U(n,f), E n = 14 MeV, linear (upper frame) and logarithmic (lower frame) scale. GEF result (redpoints) in comparison with JEFF-3.1.1 (black symbols).FIG. 45. Mass yields of U(n,f), E n = 14 MeV, linear (upper frame) and logarithmic (lower frame) scale. GEF result (redpoints) in comparison with JEFF-3.3 (black symbols). We would like to stress that a calculation with a sharp ”mean” or ”representative” value of the incident neutronenergy deviates appreciably from the ”exact” result, obtained with the full energy distribution.
B. Problems and proposed solutions
In this section, we compare the fission yields from different evaluations and from some LOHENGRIN experimentswith the GEF results in cases of severe discrepancies. The comparisons are shown for all evaluations among the three38
Problems and proposed solutions VI COMPARATIVE STUDY
FIG. 46. Initial excitation energies of the fission events in fission of
U in a PWR, rebinned from [80]. The GEF calculationswere performed with a series of sharp energy values in the centres of the bins.FIG. 47. Mass yields of
U(n fast ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with ENDF/B-VII (black symbols). considered in this work, which are available for the respective system. A =129 yield of U(n th ,f) As a semi-empirical model, GEF relies on reliable and accurate data. The inclusion of erroneous data in theadjustment of GEF parameters leads to an aberrant behavior and to false predictions of the model. As an illustrationfor these difficulties, we have a closer view on the mass yield of A = 129 in the thermal-neutron-induced fission of U.Table III shows that the measured and the evaluated values scatter strongly: The highest value is larger by a factorof 1.5 than the smallest one, while the indicated uncertainties of the different values are in the order of 5% to 10%. Insuch cases, the evaluator or the developer of a semi-empirical model must make a decision on how to treat these data.For example, the uncertainty could be increased, the data could be disregarded completely, or a personal choice on thebasis of additional arguments could be performed. Therefore, in an evaluation as well as in a semi-empirical model,there is unevitably a portion of subjective influence and decision. In fact, GEF is less vulnerable than an evaluation,because the inherent regularities help to identify such problematic cases, like the one illustrated in Table III. In thisspecific case, a singular value deviates strongly from the GEF results, while the neighboring mass yields show goodagreement. This behavior is in sharp conflict with the concept of fission channels, which extend over several masses39
Problems and proposed solutions VI COMPARATIVE STUDY
FIG. 48. Mass yields of
U(n fast ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.1.1 (black symbols).FIG. 49. Mass yields of
U(n fast ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.3 (black symbols). and, thus, exludes sharp local fluctations of this kind. Following this reasoning, figures 9, 10 and 11 suggest that thelarger values given in Table III are the more reliable ones .In the determination of the parameters of GEF-Y2019/V1.2, the mass yield of A = 129 in U(n th ,f) was disre-garded. 40 Problems and proposed solutions VI COMPARATIVE STUDY
TABLE III. Empirical values for the A = 129 yield of U(n th ,f).Value Uncertainty Reference0.610 4.9% [82]0.804 5.0% [83]0.817 5.8% [84]0.543 0.045 (8.3%) ENDF/B-VII.00.543 0.045 (8.3%) ENDF/B-VIII.00.706 0.037 (5.2%) JEFF-3.1.10.814 0.058 (7.1%) JEFF-3.30.978 0.18 (18%) GEF-2019/1.2Note: Selection of measured and evaluated mass yields for a case with large scattering. The GEF estimation is listed inaddition.
2. Mass yields of
Th(n th ,f) In figure 50, the mass yields of the system
Th(n th ,f) in ENDF/B-VII deviate strongly from the GEF resultsalmost over the whole distribution. In particular, in view of the relatively good reproduction of the mass yields ofthe close system Th(n th ,f), the shape proposed by ENDF/B-VII seems to be erroneous. We recommend to replacethe mass yields, in particular between the asymmetric peaks, by the GEF results.
The relative yield of the symmetricfission channel, however, remains somewhat uncertain.
FIG. 50. Mass yields of
Th(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with ENDF/B-VII (black symbols).
3. Mass yields of
U(n th ,f) In figure 51, the mass yields of the system
U(n th ,f) in ENDF/B-VII deviate strongly from the GEF result in thewings at extreme mass asymmetry. We recommend to replace the mass yields for
A < and for A > by the GEFresults. Problems and proposed solutions VI COMPARATIVE STUDY
FIG. 51. Mass yields of
U(n th ,f), linear (upper frame) and logarithmic (lower frame) scale, GEF result (red points) incomparison with ENDF/B-VII (black symbols).
4. Mass yields of
U(n th ,f) In figure 52, the mass yields of JEFF-3.3 are compared with the GEF results. Apart from the discrepancy of themass yields near symmetry, which may be explained by the fact that
U is again thermally not fissile, there is aclear shift in almost all the wings of the mass-yield distribution of the system
U(n th ,f). We recommend to replacethe discrepant values by the GEF results.
FIG. 52. Mass yields of
U(n th ,f), linear (upper frame) and logarithmic (lower frame) scale, GEF result (red points) incomparison with JEFF-3.3 (black symbols). Problems and proposed solutions VI COMPARATIVE STUDY
5. Mass yields of
Np(n th ,f) In figure 53, there is a clear shift in the right wing of the light peak between GEF and ENDF/B-VII in the mass-yielddistribution of the system
Np(n th ,f) and some discrepancy in the whole light peak. This problem has already beenmentioned in Ref. [28]. It has been attributed to a target contamination, probably of Pu. Figures 54 and 55 showthat this problem does not appear in the JEFF evaluations , probably by the use of some more recent data.
FIG. 53. Mass yields of
Np(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with ENDF/B-VII (black symbols).FIG. 54. Mass yields of Np(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.1.1 (black symbols). Problems and proposed solutions VI COMPARATIVE STUDY
FIG. 55. Mass yields of
Np(n th ,f), linear (upper frame) and logarithmic (lower frame) scale, GEF result (red points) incomparison with JEFF-3.3 (black symbols).
6. Mass yields of
Pu(n th ,f) In figures 56, 57, and 58 there is good agreement between the GEF results and ENDF/B-VII for mass yields of thesystem
Pu(n th ,f). However, the evaluations JEFF-3.1.1 and JEFF-3.3 show strong discrepancies near symmetryand in the upper wing. We recommend to use the ENDF/B-VII compilation or the GEF results.
FIG. 56. Mass yields of
Pu(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with ENDF/B-VII (black symbols). Problems and proposed solutions VI COMPARATIVE STUDY
FIG. 57. Mass yields of
Pu(n th ,f), linear (upper frame) and logarithmic (lower frame) scale, GEF result (red points) incomparison with JEFF-3.1.1 (black symbols).FIG. 58. Mass yields of Pu(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with JEFF-3.3 (black symbols).
7. Mass yields of
Cf(n th ,f) In figure 59, there are important discrepancies between the mass yields of ENDF/B-VII and the GEF results forthe system
Cf(n th ,f), while in figure 60 the data of the LOHENGRIN experiment [85] agree on a coarse scale quitewell with the GEF results. On a finer scale, however, the LOHENGRIN data show erratic fluctuations, which aremuch larger than the given uncertainties. Such fluctuations are not found in the fission yields of any other system.Therefore, we attribute the fluctuations to difficulties in the experiment or in the data analysis. We recommend touse the GEF results. Problems and proposed solutions VI COMPARATIVE STUDY
FIG. 59. Mass yields of
Cf(n th ,f), linear (upper frame) and logarithmic (lower frame) scale, GEF result (red points) incomparison with ENDF/B-VII (black symbols).FIG. 60. Mass yields of Cf(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with a LOHENGRIN [85] experiment (blue symbols).
8. Mass yields of
Es(n th ,f) In figure 61, there are strong discrepancies in the whole mass distribution between GEF and ENDF/B-VII for
Es(n th ,f). It is rather speculative to argue, which set of mass yields is more reliable. It is, however, rather difficultto reconcile the fission yields from ENDF/B-VII with the inherent regularities of the GEF model. Problems and proposed solutions VI COMPARATIVE STUDY
FIG. 61. Mass yields of
Es(n th ,f), linear (upper frame) and logarithmic (lower frame) scale, GEF result (red points) incomparison with ENDF/B-VII (black symbols).FIG. 62. Mass yields of Fm(n th ,f), linear (upper frame) and logarithmic (lower frame) scale. GEF result (red points) incomparison with ENDF/B-VII (black symbols). Problems and proposed solutions VI COMPARATIVE STUDY
9. Mass yields of
Fm(n th ,f) In figure 62 there are strong discrepancies in the whole mass distribution between GEF and ENDF/B-VII for
Fm(n th ,f). In particular, the mean value of the distribution is shifted by about 3 units. This entails a drasticdifference in the mean number of prompt neutrons, where the deduced ENDF value deviates strongly from thesystematics, see Ref. [28]. We recommend to replace the whole distribution by the GEF results.
C. Quantitative analysis
The preceding sections revealed numerous discrepancies between the mass yields from different evaluations, selectedkinematical experiments and the results of the GEF code. By analyzing the graphical presentations of the full massdistributions, conjectures on the origin of many observed deviations were given. As a complementary quantitative butlumped information, Table IV presents the RMS values of the deviations per degree of freedom (reduced chi-squarevalues) between fission-product mass yields from GEF and values from different evaluations and from LOHENGRINexperiments.The values extend over a large range. The highest ones are found for cases, where indications for severe shortcomingsof the evaluated or measured data were found, for example for thermal-neutron-induced fission of
Th, U, Es,
Fm and, to a lesser degree,
Pu,
Cf and
Cf. The observed problems of GEF in reproducing the yields in thelight peak for fission of thorium and uranium isotopes, which are given with rather small uncertainties, are reflectedby relatively large chi-square values of up to about 5.However, a few peculiarities must be taken into account when interpreting the numbers. For example, it seems thatthe uncertainties of the ENDF/B-VII evaluation are estimated rather conservatively, leading to rather low chi-squarevalues. On the other hand, the uncertainties attributed to the yields measured at LOHENGRIN are very small, whichleads to relatively high chi-square values. Maybe these uncertainties do not fully consider the systematic uncertaintiesof this method. In addition, the use of symmetric uncertainties on a linear scale in our calculation, also for very smallyields, is not realistic. Asymmetric uncertainties or symmetric uncertainties on a logarithmic scale would have beenmore adapted.
D. Summary
The comparative study of the preceding sections gives the following result for thermal-neutron-induced fission: Infifteen cases, good or at least satisfactory agreement is obtained between the mass yields from GEF and the empiricaldata. In eight cases, severe discrepancies appeared, most of them hinting to erroneous evaluations, according toour analysis. The yields at symmetry in the low-energy fission of the actinides show deviations in several systems.They pose specific difficulties to both the evaluations and the GEF code due to large experimental uncertainties inthe measurement of low yields and due to the influence of weak shells on the depth of the symmetric fission valley,respectively. Additional problems, especially at mass symmetry, arize from the broad energy distribution of ”thermal”reactor neutrons, in particular for thermally not-fissile nuclei. Most of the LOHENGRIN experiments seem to be muchmore accurate than the evaluations. The agreement of the mass yields with the GEF results tends to confirm thesmall indicated uncertainties of these experiments, except in the case of
Cf(n th ,f). The LOHENGRIN data forma backbone for determining the parameters of GEF. However, this is not a direct adjustment. On the contrary, thecompatibility of the LOHENGRIN results with the regularities and constraints of the theoretical framework of basicconcepts and laws of general validity in the GEF model tends to corroborate both the LOHENGRIN data and the GEFmodel. Thus, the evaluations can be improved by including the LOHENGRIN data to a greater extent. The remainingdeviations between empirical mass yields and GEF results reveal some deficiencies of both the evaluations and GEF,depending on the case. Local deviations for individual systems hint more to a problem in the evaluations, whilegeneral deviations for several neighboring systems hint more to a problem in GEF. In many cases where satisfactoryagreement with the GEF result is found, but the uncertainties of the evaluations are very large, the GEF results maybe included in the evaluation process and help to improve the accuracy of the evaluated mass yields. Thus, the presentcomparative study can be exploited to improve the evaluations leading to enhance the quality of nuclear data. It alsoprovides information on a few remaining deficiencies of the GEF code, which call for further refinements. This is avery important issue for the estimation of the characteristics of the antineutrino production, where the requirementson accuracy are extremely high.We have learned that the adjustment of GEF parameters to empirical data is a rather difficult task. Indeed,performing a least-squares fit to all data does not lead to a satisfactory result, because many evaluated values areerroneous. In some cases, this is evident, but in the majority of cases a careful analysis and a systematic comparison48 Summary VI COMPARATIVE STUDY
TABLE IV. RMS values of the deviations between fission-product mass yields from GEF and values from the evaluationsENDF/B-VII, JEFF-3.1.1 and JEFF-3.3 as well as from LOHENGRIN experiments.System ENDF JEFF-3.1.1 JEFF-3.3 Lohengrin
Th(n th ,f) 420/140 — — — Th(n th ,f) 4.9/3.6 — — 17/4.2 U(n th ,f) 1.2/31 — — — U(n th ,f) 1.3/4.0 5.1/3.7 4.2/3.7 26/4.5 U(n th ,f) 3.8/1.1 5.4/1.0 4.4/0.96 4.8/0.93 U(n hi ,f) 0.51/8.3 3.7/10.8 3.7/9.3 — U(n th ,f) 24/50 — — — U(n fast ,f) 0.34/1.6 5.1/1.6 2.3/1.5 —
U(n hi ,f) 0.27/4.4 2.2/7.6 2.3/6.8 — Np(n th ,f) 0.69/21.7 2.5/4.0 1.4/3.5 — Np(n th ,f) — 2.2/4.6 5.7/2.5 8.8/3.2 Pu(n th ,f) — 3.7/9.5 13.1/7.1 — Pu(n th ,f) 0.37/1.4 2.0/2.2 1.7/1.5 9.2/0.74 Pu(n th ,f) 0.59/4.9 — — — Pu(n th ,f) 0.53/1.1 6.3/15.7 6.1/17.2 — Pu(n th ,f) 0.49/4.06 — — — Am(n th ,f) 3.7/3.0 2.2/4.4 1.6/3.6 — Am(n th ,f) 0.5/1.7 1.2/2.4 — — Am(n th ,f) — 2.6/14.7 5.2/2.3 — Cm(n th ,f) 1.4/14 4.1/13 2.4/7.3 — Cm(n th ,f) — 2.7/15.4 0.6/2.0 — Cm(n th ,f) 0.51/4.1 1.5/5.1 1.1/3.5 — Cf(n th ,f) 1.0/5.6 — — 27/1.8 Cf(n th ,f) 10/19 — — 16/21 Es(n th ,f) 33/74 — — — Fm(n th ,f) 13/42 — — —Note: Two numbers are given. The first one uses the uncertainties of the evaluation, respectively experiment. The second oneuses the uncertainties from GEF. Masses with calculated or evaluated, respectively experimental, yields below 0.01 percent arenot considered. n th means thermal neutrons, n fast means fast neutrons, and n hi means neutrons of 14 MeV. between data from different sources and evaluations and with GEF is needed to sort out the more reliable and the lesstrustworthy values.Eventually, we came up with the following rules:1. Radiochemical data have very different quality. As demonstrated in section VI, by far the most reliable ones arethe FY for U(n th ,f), followed by Pu(n th ,f) and very few other systems. The data of all other systems are lesstrustworthy due to large uncertainties of the measured yields or lacking data for a number of masses. The quality isnot always reflected by the error bars.2. Mass yields from LOHENGRIN experiments are much more accurate than those from radiochemical measure-ments (with one exception, see paragraph VI B 7).3. Indirect information on FY (antineutrino spectrum, decay heat etc.) are extremely sensitive probes for the overallquality of the FYs for specific systems.4. It is important to primarily adjust the parameters of GEF to the most trustworthy data. The regularities ofGEF help to recognize faulty data of other systems.The results of applying them have been shown above. 49 SummaryVII PREDICTIONS OF ANTINEUTRINO ENERGY SPECTRA BASED ON THE GEF FISSION YIELDS
TABLE V. List of the 20 nuclides contributing most importantly to the the
U antineutrino spectrum in the 4 to 5 MeVbin ordered by importance of contribution obtained with the fission yields of JEFF-3.1.1. In the second and third columnsare indicated the absolute relative discrepancy of the GEF fission yields to the JEFF-3.1.1 and JEFF-3.3 evaluated cumulativeyields. Nuclide Rel. Dif. GEF vsJEFF-3.1.1 Rel. Dif. GEF vsJEFF-3.339-Y-95 5.4% 6.5%39-Y-94 9.4% 9.5%38-Sr-93 0.6% 0.4%55-Cs-139 2.8% 3.9%55-Cs-140 2.8% 0.23%57-La-142 2.1% 2.4%41-Nb-98 5.7% 5.8%37-Rb-91 9.4% 5.7%41-Nb-100 1.2% 2.8%57-La-144 9.0% 9.0%38-Sr-95 7.6% 6.7%54-Xe-139 3.6% 5.1%41-Nb-101 0.2% 3.3%36-Kr-90 12.3% 8.9%55-Cs-141 2.0% 3.1%37-Rb-92 0.02% 10.5%39-Y-96 25.9% 27.5%37-Rb-89 4.2% 4.8%36-Kr-89 3.9% 4.0%37-Rb-90 6.0% 2.6%
VII. PREDICTIONS OF ANTINEUTRINO ENERGY SPECTRA BASED ON THE GEF FISSIONYIELDSA. Beta-decay emitters
Using the summation method and GEF fission yields, the nuclei contributing mainly to the antineutrino energyspectra of the most dominant isotopes in a reactor core can be extracted in bins of antineutrino energies as it wasdone in the past from [86] with the summation method of [21] obtained with the JEFF3.1.1 fission yields.Table V shows the relative discrepancies between the GEF, JEFF-3.1.1 and JEFF-3.3 cumulative yields for the toptwenty of the largest contributions to the
U antineutrino energy spectrum obtained with the summation method [23].The agreement reached after the complex tuning of the GEF model on the available datasets for a wide set of fissioningsystems is quite satisfactory, and mainly constrained by the small uncertainties of the LOHENGRIN data. As shownin section VI, the LOHENGRIN fission yields are in good agreement with the JEFF evaluated fission yields in thecase of
U, but their uncertainties are smaller, which lets us think that the uncertainties of the JEFF yields couldbe reduced.Figure 63 shows the relative ratio of the antineutrino energy spectra of U, Pu,
Pu and
U obtained withthe cumulative yields computed using the GEF code in its latest version to those obtained either with the cumulativefission yields of JEFF-3.1.1(red line) or JEFF-3.3 (blue line). An agreement at the 2% level is observed with JEFF-3.1.1 up to 4 MeV in the four cases. The agreement is also good with JEFF-3.3 though it deviates by 3% above 3 MeVin the case of
U. Above 4 MeV, larger deviations can be observed reaching 4% around 5.5 MeV in the
U and 3%in the
Pu ratios. In the cases of
Pu and
U, the discrepancies between the two sets of JEFF fission yields arenoticeable above 3 MeV, with the largest deviation reached in the case of the JEFF-3.3 yields of the
Pu. Specialcare was taken for using a realistic effective energy distribution of the impinging neutrons for the calculation of themass yields for the fission of
U induced by fast neutrons.Overall, the level of agreement now reached between the spectra obtained with the GEF predictions and thatobtained with the evaluated fission yields has been greatly improved by the adjustment of GEF to empirical dataperforming a survey on the FYs of all the systems.In order to compare the GEF prediction of antineutrino spectra with reactor neutrino experiments, it is necessaryto fold the spectra with the detection reaction, the Inverse Beta Decay (IBD) process, historically used in the firstexperimental evidence of the neutrino by Reines and Cowan [2]. The IBD process is the result of the interaction50
Beta-decay emittersVII PREDICTIONS OF ANTINEUTRINO ENERGY SPECTRA BASED ON THE GEF FISSION YIELDS
FIG. 63. Ratio of the antineutrino spectra calculated with yields from GEF and from the fission-yield libraries (FYL) JEFF-3.1.1, respectively JEFF-3.3, after tuning.FIG. 64. Comparison of the Inverse Beta Decay yields as a function of the fission fraction of
Pu obtained by the Daya Bayexperiment [87] (see text) with summation-model predictions in which the decay data are those of [23] and the fission yieldsare the cumulative ones from the new version of the GEF code presented here, from the JEFF-3.1.1 database and from theJEFF-3.3 database. of an ¯ ν e with a proton, producing a positron and a neutron (reaction threshold 1.8 MeV). In Figure 64, the inversebeta decay yield as a function of the amount of fission events in the reactor coming from Pu (F , called “fissionfraction”) published by the Daya Bay collaboration [87] and defined following the equation σ f ( F ) = ¯ σ f + dσ f dF ( F − ¯ F ) (3)is displayed with open diamonds (the data points include error bars). In this formula, the average IBD yield ¯ σ f isobtained by folding the IBD cross-section with the total antineutrino energy spectrum computed by weighting the U, U, Pu and
Pu spectra by their average fission fractions provided in [87]. ¯ F is the average Pu fissionfraction, and dσ f dF is the change of the IBD yield per unit Pu fission fraction.In [23], the latest predictions performed with the summation model (SM) updated with the TAGS measurementsperformed during the last decade predict an IBD yield located only 1.9% above the IBD yield measured by Daya Bay,51
Beta-decay emittersVII PREDICTIONS OF ANTINEUTRINO ENERGY SPECTRA BASED ON THE GEF FISSION YIELDS and a slope of its evolution with F in very good agreement with the experimental one. In this SM, the individualfission yields from the JEFF-3.1.1 database are evolved at 450 days of irradiation with the MURE code (dashed linecalled SM-18 in Fig. 64), taking into account the evolution due to the various half-lives of the fission products andneutron capture. In order to see how the predictions of the SM using the same beta decay data but cumulative yieldsfrom the evaluated JEFF database in its 3.1.1 and 3.3 versions and the cumulative yields from the new version ofthe GEF code presented in this article would compare with the Daya Bay results, we have computed the associatedIBD yields. They are displayed in Fig. 64 with respectively orange, red and black lines. The discrepancy between theSM-18 and the yellow line (cumulative yields from JEFF-3.1.1) arises only from the use of cumulative yields insteadof evolved individual fission yields. Indeed in the cumulative yields, a few very long-lived nuclei are assumed to havereached equilibrium whereas they should not have after 450 days. This gives rise to about a 0.4% over-estimate of theIBD yields, due to the use of cumulative yields. In addition, one can see that using the JEFF-3.3 cumulative yields,the IBD yields obtained are slightly above the ones obtained with the JEFF-3.1.1 version of the fission yields database. B. Antineutrino energy spectra
FIG. 65. Calculated antineutrino spectra from GEF combined with the selection of decay data of [23] for 6 isotopes of Th ( Z = 90) in the case of thermal fission. We have mentioned in the previous sections that there are indeed discrepancies between the two versions of theJEFF fission yields database, which are not always well understood. This reflects into the antineutrino spectra (see forinstance the differences observed for
U and
Pu). It is not obvious to us that the fission yields of JEFF-3.3 shouldbe used systematically instead of the ones of JEFF-3.1.1. For instance in the case of
Pu for which inconsistencies inthe evaluation of the fission yields have been evidenced in section VI B 6, the antineutrino energy spectrum computedwith the JEFF-3.3 fission yields departs from the one computed with GEF above 4 MeV (see Fig. 63). Overall, theSM model using the cumulative yields from GEF lies about 1% above the SM-18 prediction (but one would have tocorrect the result for the impact of the very long-lived nuclei, i.e. a -0.4% effect on the IBD yield) and about 0.7%above the JEFF-3.1.1 cumulative yields. This result shows that GEF is an excellent model for the prediction of fissionyields for antineutrino fundamental and applied physics, accurate enough to be competitive with evaluated databaseseven in the case of the most well known thermal fissioning systems and to be compared with neutrino experiments.The antineutrino energy spectra for the systems listed in the first part of this article have been computed usingthe GEF cumulative fission yields combined with the set of beta decay data described above [23]. They are shownin Figs. 65, 66, 67, 68, 69, 70, 71 for the systems Z = 90, Z = 92, Z = 93, Z = 94, Z = 95, Z = 96 and Z = 98,respectively, in case of thermal fission.For the specific case of U, which undergoes fast-neutron-induced fission, we have considered two cases: fissionwith 2 MeV incident neutrons and fission with an energy distribution of the incident neutrons, which follows theprescription of [80] (cf. Fig. 46). The calculations in this section for all other target nuclei are performed assumingfission induced by thermal neutrons, also for those target nuclei, which are thermally not-fissile. A detailed view on theadditional effect of energy-dependent fission cross sections, which depends on the reactor type, is beyond the scope ofthis work. (From section VI it may be assumed that it is small in most cases, except for
U.) This way, a clear viewon the influence of global and structural features of the fission process itself and of the radioactive-decay properties52
Antineutrino energy spectraVII PREDICTIONS OF ANTINEUTRINO ENERGY SPECTRA BASED ON THE GEF FISSION YIELDS
FIG. 66. Calculated antineutrino spectra from GEF combined with the selection of decay data of [23] for seven isotopes of U( Z = 92) in the case of thermal fission except for U. The prediction for the fast-neutron-induced fission of
U is given foran input neutron energy distribution which follows the prescription of [80].FIG. 67. Calculated antineutrino spectra from GEF combined with the selection of decay data of [23] for seven isotopes of Np( Z = 93) in the case of thermal fission. on the production of antineutrinos and other particles is obtained.The corresponding tables containing the datapoints of the spectra are provided as supplemental material to thispaper. These spectra can be used to compute the antineutrino energy spectra of future reactors loaded with varioustypes of fuels in the frame of non-proliferation scenario studies. A big advantage of this set of spectra is the consistencybrought by the use of the same model to compute the fission yields of all fissioning systems. This consistency could notbe attained with the current evaluated fission yield datasets for the variety of fissioning systems that are needed fornon-proliferation studies because of the lack of underlying experimental data and because of the remaining problemsin the data listed in the paragraphs above. In the frame of the comparisons of diversion scenarios versus legitimateuse of a given type of nuclear reactor [29], the fission yield covariance matrices provided by GEF make it possible tocomputate the uncertainties for the corresponding antineutrino emissions.With the sets of fissioning systems provided in this article, studies of the antineutrino emission of reactors loadedwith thorium/uranium fuel such as CANDU reactors, or studies of Generation-IV breeders including blankets loadedwith minor actinides or of ADS loaded with assemblies containing nuclear wastes for transmutation purposes arepossible. The spectra provided in this article are computed for fission induced by thermal neutrons. The studyof the fast-neutron-induced fission yields of U presented in the section VI A 2 has shown that a more accuratedetermination of the fission yields could be obtained by taking into account their dependence on the neutron energyspectrum in the reactor in the fission process, a dependenceF that has an influence on the antineutrino emission as wecould observe in the case of the fast-neutron-induced fission of
U. This is the reason why we would recommend to53
Antineutrino energy spectraVII PREDICTIONS OF ANTINEUTRINO ENERGY SPECTRA BASED ON THE GEF FISSION YIELDS readers interested in fast-neutron-induced fission to use the neutron energy distribution of the studied reactor designin the calculation of the corresponding fission yields with GEF.
FIG. 68. Calculated antineutrino spectra from GEF combined with the selection of decay data of [23] for seven isotopes of Z = 94 in the case of thermal fissions.FIG. 69. Calculated antineutrino spectra from GEF combined with the selection of decay data of [23] for seven isotopes of Z = 95 in the case of thermal fissions. We have performed a quick systematic study of the antineutrino spectra presented in the Figs. 65, 66, 67, 68, 69, 70and 71. In the following, the specific case of
U is considered to be beyond the scope of the present work, whichfocuses on thermal fission. It will be addressed in a future publication.The antineutrino emitted fluxes per fission corresponding to isotopic chains of the fissioning systems are presentedin Fig. 72 as a function of the A over Z ratio of the fissioning nucleus. They all show a generic linear trend on which anodd-even effect is superposed. A linear trend has already been shown in Fig. 4 of [22] where the detected antineutrinoflux was plotted as a function of (3 Z - A ) for a set of fissioning systems. In this figure, the detected antineutrino fluxesnearly align, but some deviations could be observed. The odd-even effect observed in Fig. 72 is one of the reasons ofthe deviations observed in [22]. In Fig. 72, two linear fits could be performed for the sets of odd or even isotopes ofeach element. In addition, the emissions of some isotopic chains are very close to each other as a function of N over Z .This is the case for thorium, uranium and neptunium, and then plutonium, americium and curium. The bottom plotof Fig. 72 shows the same antineutrino fluxes but plotted as a function of A , which makes the figure easier to read. Thelinear trend for each isotopic chain appears more clearly as the scale makes the odd-even effect appearing smaller. Thelines are quasi-parallel showing that the increase of the neutron number of the fissioning nucleus directly impacts theneutron number of the fission products. The number of emitted antineutrinos per fission follows directly the differencein N over Z between the post-neutron fission products and the stability valley. This implies a strong correlation with54 Antineutrino energy spectraVII PREDICTIONS OF ANTINEUTRINO ENERGY SPECTRA BASED ON THE GEF FISSION YIELDS
FIG. 70. Calculated antineutrino spectra from GEF combined with the selection of decay data of [23] for seven isotopes of Z = 96 in the case of thermal fissions.FIG. 71. Calculated antineutrino spectra from GEF combined with the selection of decay data of [23] for six isotopes of Z =98 in the case of thermal fissions. the N over Z ratio of the fissioning system, a correlation that we find to be linear. From this generic study, it is easyto extrapolate the values of antineutrino fluxes to fissioning systems for which neither data nor calculation exist.For comparison, the delayed-neutron fractions and the number of prompt neutrons per fission associated withdifferent fissioning systems were computed with GEF as well. In Fig. 73, the delayed-neutron fractions per fissionshow a behavior similar to that of antineutrinos, except that their increase with N over Z is not linear. This couldbe explained by the fact that only the neutron-richest nuclei are β -n precursors. Moreover, the odd-even effect alongisotopic chains is less pronounced. 55 Antineutrino energy spectraVII PREDICTIONS OF ANTINEUTRINO ENERGY SPECTRA BASED ON THE GEF FISSION YIELDS
FIG. 72. Top: emitted antineutrino flux corresponding to the spectra of Fig. 65, 66, 67, 68, 69, 70, 71 obtained with the fissionyields from GEF combined with the selection of decay data of [23] for different systems as a function of the N over Z ratio ofthe fissioning system. Bottom: same but plotted as a function of A .FIG. 73. Delayed-neutron fractions computed with GEF for different systems as a function of the N over Z ratio of the fissioningsystem.FIG. 74. Prompt neutron multiplicities computed with GEF for different systems as a function of the N over Z ratio of thefissioning system. Antineutrino energy spectraVII PREDICTIONS OF ANTINEUTRINO ENERGY SPECTRA BASED ON THE GEF FISSION YIELDS
FIG. 75. Individual beta decay contributions of fission products from the reactions
U(n th ,f), U(n fast ,f),
Pu(n th ,f) and Pu(n th ,f) calculated with the GEF code. The size of the black circles, which shrink to points towards increasing neutronexcess, is proportional to the logarithm of the magnitude over four orders of magnitude, and the color indicates the Q-valuerange. Antineutrino energy spectraVII PREDICTIONS OF ANTINEUTRINO ENERGY SPECTRA BASED ON THE GEF FISSION YIELDS
The delayed-neutron fractions of uranium and neptunium isotopes, as well as those of plutonium and americium arealmost identical. This is explained by the fact that the odd-even effect in fission-product Z is much larger for even- Z fissioning systems. Thus, the relative production of odd- Z fission products is enhanced for odd- Z fissioning systems.Due to the enhanced beta Q value of odd- Z fission products, the delayed-neutron fractions for odd- Z fissioningsystems are so much enhanced that the average decrease of the delayed-neutron fraction for fixed N over Z by theincrease of Z by one unit is just compensated. This way the values of the even- Z uranium and the neighboring odd- Z neptunium as well as the values of the even- Z plutonium and the neighboring odd- Z americium become very close.In more detail, also the enhanced fission Q values for odd- Z fissioning systems that lead to slightly less neutron-richfission products and to a reduction of the delayed-neutron fractions (see next paragraph) must be considered.The number of prompt neutrons per fission for four isotopic chains are plotted in Fig. 74. Their behavior deviatesfrom that of antineutrinos and delayed neutrons. The prompt-neutron multiplicity is most sensitive to the Z ofthe fissioning system and shows only a moderate increase along the isotopic chains. This corresponds to the linearincrease of the total fission-fragment excitation energy with Z /A / , postulated by Asghar and Hasse [88] on thebasis of macroscopic nuclear properties. The odd-even staggering of the prompt-neutron multiplicity as a function ofneutron number is clearly evidenced. The largest values of prompt neutrons per fission are obtained for odd- N fissiontargets.The staggering can be explained as follows: With respect to the smooth variation, even- N target isotopes are morebound than odd- N isotopes by the pairing energy ∆ N , and, in addition, their neutron separation energy is higher by2∆ N . This leads to a systematically higher fission Q value for odd- N target nuclei by ∆ N in thermal-neutron-inducedfission and a corresponding larger number of prompt neutrons. It is assumed that most of this staggering appearsin the total excitation energy of the fission fragments, although some odd-even staggering might also be present inthe total kinetic energy by the breaking of nucleon pairs during the fission process according to an idea of Ref. [73].This effect is included in GEF. However, measured prompt-neutron multiplities may show weaker staggering, becausemany even- N nuclei are thermally not-fissile. In these cases, the observed fission events may be induced by neutronsof higher energies, depending on the experimental conditions, like discussed in section VI A 2 in the case of U.Since delayed neutrons and antineutrinos originate both from the radioactive decay of the fission products while theprompt neutrons arise from the de-excitation of the fission fragments, a similar trend is awaited in the behavior of thetwo first observables. The main difference between the two is that the delayed-neutron precursors are less numerousthan the antineutrino emitters, making the antineutrino emission more sensitive to the fission yield distribution in itsentirety.The comparative view on the characteristics of antineutrinos, prompt and delayed neutrons demonstrates the com-plexity of global trends and structural properties of these three observables. In particular, it calls into question anylinear interpolation or extrapolation of trends deduced from scarce or incomplete experimental data.Altogether, the results in this section demonstrate that the antineutrino observable is directly linked to the fissionprocess, and an improved experimental knowledge of the antineutrino emission could help understanding the fissionprocess itself.
C. Sensitivity to the fission product distributions from different systems
In addition to calculating the so-far presented yields of the secondary fission products resulting from the de-excitationof the primary fragments produced at scission, the GEF model can compute their radioactive decay whenever it applies.Hence, the code can provide a complete overview of the contributions of the various fission products to the Q valuedistribution of beta decays. Fig. 75 shows the calculated intensities and Q values of the beta decays for the foursystems
U(n th ,f), U(n fast ,f),
Pu(n th ,f) and Pu(n th ,f) on the chart of the nuclides.The highest decay energies are generally found in the light fission-product group with an odd-even staggering thatenhances the decay energies of the odd elements. A detailed analysis of the results of the calculation shows that highdecay energies (above 9 MeV) and presumably also the high-energy part of the antineutrino spectrum are dominatedby contributions of the odd- Z elements from Z = 33 to Z = 37.As expected, one observes a shift to more exotic nuclides with a tendency to longer beta-decay chains with increasingneutron excess of the fissioning system. This goes in line with an enhancement of higher decay energies. U(n fast ,f)provides the highest contributions to the high-energy part of the spectrum, because it is the most neutron-rich system.A detailed comparison of this piece of information with that on the accuracy of the fission-product yields, discussedin the preceding sections, provides a good basis for revealing the contributions of individual fission-yield uncertaintiesto the uncertainties of calculated antineutrino spectra.The possible application of antineutrino spectroscopy for reactor monitoring depends essentially on the sensitivityof the antineutrino energy spectrum to the fissioning system. A first glance on this sensitivity can be obtained byaccumulating the Q values of the consecutive beta decays of the fission products with their respective appearances.58
III CONCLUSION
FIG. 76. Antineutrino multiplicity as a function of the Q value of the consecutive beta decays of the fission products for thesystems
U(n th ,f), U(n fast ,f),
Pu(n th ,f), and Pu(n th ,f), calculated with the GEF code. For clarity, the spectrum isshown with a coarse binning of 500 keV. This signature has the advantage of not being influenced by the branchings of the beta decay to excited levels. Thiscould introduce a bias, because the experimental knowledge on these branchings is systematically less detailed for themore neutron-rich nuclei.Fig. 76 shows the accumulated distribution of Q-values for
U(n th ,f), U(n fast ,f),
Pu(n th ,f), and Pu(n th ,f).Obviously, there is a systematic and rather important increase of the antineutrino multiplicity, in particular at higherenergies, with increasing A/Z of the fissioning system as was observed in the section VII B. Because the relativeenhancement is energy dependent, the shape of the antineutrino energy spectrum is sensitive to the relative contribu-tions of the different fissioning systems. Combining this information with the expected uncertainty of the measuredantineutrino energy spectrum will provide a good estimation of the sensitivity of antineutrino spectroscopy for reactormonitoring in specific cases. A more detailed quantitative study is beyond the scope of the present work, which islimited to prove that GEF provides the necessary tools for such a work.
VIII. CONCLUSION
The calculation of the antineutrino production in fission product decay is presently one of the most demandingapplications of nuclear data due to the required high accuracy. This is true for both antineutrino physics and spec-troscopy for reactor monitoring. In this work, it was shown that the presently reached quality of related nuclear data,in particular of the fission yields, can appreciably be improved by exploiting and combining different approaches:traditional radiochemical experiments, kinematic experiments and suitable theoretical models. For the first time, acareful analysis and a systematic comparison between data from different sources and evaluations and with GEF havebeen performed to sort out the more reliable and the less trustworthy values, thus assisting the evaluation process.Examples were shown of how erroneous data in different evaluations, up to very recent ones, can be detected andrather credible estimations of un-measured values can be performed. In a number of cases, our recommendations weregiven to replace apparently erroneous data by more realistic estimations.As a result of this work, the level of agreement attained on the antineutrino energy spectra computed with the newGEF fission yields in comparison with the JEFF evaluated fission yields has been remarkably improved in the case ofthe four main fissioning systems in actual reactors. Predictions performed with the summation method using the GEFcumulative fission yields show that the new version of GEF (GEF-Y2019/V1.2) has reached a level of predictivenessof the Inverse Beta Decay yields at the percent level with respect to the one of the JEFF-3.1.1 evaluated fission yieldsand only 2.5% above the Daya Bay IBD yields once corrected from the contribution of the very long-lived nuclei.This excellent agreement with the results obtained using the JEFF-3.1.1 and JEFF-3.3 fission yields as well as theindications for realistic GEF-based uncertainty estimates for the most important fissioning systems open the newpossibility to propagate the latter from GEF to the antineutrino spectra.A systematics of calculated intensities and beta Q values of all fission products for the four most important fissioningsystems, contributing to the antineutrino production in a fission reactor, reveals some prevailing characteristics of theunderlying fission and radioactive-decay processes. These are crucial for estimating the sensitivity of a possibleapplication of antineutrino production to reactor monitoring. Predictions of antineutrino energy spectra based on theGEF fission yields combined with the most recent decay data sets from [23] are provided for a list of fissioning systems59
III CONCLUSION which could be used in the frame of such sensitivity studies.By extending the GEF calculations, presented in this work, with explicit calculations of the beta-decay energies,including error propagation and correlations, one obtains a powerful tool for identifying the specific problems andlimitations of the summation method that determine the quality that can presently be reached. This can also be usedfor establishing a list of most urgent improvements of the quality of underlying nuclear data.
ACKNOWLEDGEMENT
This work was supported by the University of Nantes, the CNRS/in2p3, and the NACRE project of the NEEDSchallenge by financing several research visits in 2018 and 2019. K.-H. S. thanks the SUBATECH laboratory for warmhospitality. 60
X APPENDIX
IX. APPENDIXOBSERVATIONS
Four systems were selected for a detailed comparison of the independent yields from the JEFF-3.3 evaluation andthe GEF results. These systems contribute most strongly to the antineutrino production in presently operating fissionreactors.
U(n th ,f ) U(n th ,f) is the most intensively studied reaction. Thus, the evaluated yields for this case are expected to bethe most reliable. Figs. 77 to 82 show almost perfect agreement between JEFF-3.3 and GEF for the elements withpeak yields above 1%. There are some issues in the most asymmetric wings, where the super-asymmetric (S3) modecontributes. Severe discrepancies appear for Z <
32 and
Z >
60. In both cases, the yields are overestimated; inthe second case, the isotopic distributions are shifted towards lighter isotopes in addition. The distributions nearsymmetry are rather well reproduced. However, the shape of the distribution of the Z = 48 isotopic yields fromGEF does not agree with the one from the evaluation: the height of the right peak is strongly underestimated. Anunderestimation of the left wing of the mass distributions for Z = 44 is also seen, although by a much smaller amount.However in both the evaluation and the calculation the conservation laws are fulfilled, by imposing it in the first caseand by the consistency of the model in the second case. The differences in shape of the different distributions (forthe light and the heavy fission product from GEF and from JEFF-3.1.1) can be explained by the influence of theprompt-neutron-multiplicity distribution as a function of the fission-product A and Z in these four cases.It is known that the symmetric mode is characterized by a small charge polarization and a low TKE, correspondingto a large prompt-neutron multiplicity, while the asymmetric modes (S1 and S2) in this Z range are characterizedby a large charge polarization, favoring the production of neutron-rich heavy fragments at scission, and a high TKE,corresponding to a small prompt-neutron multiplicity. With this information, one can attribute the left peak in theisotopic distribution of Z = 48 to the symmetric mode and the right peak to the asymmetric component, consistingof the S1 and S2 fission channels. Thus the contribution of the symmetric mode to the Z = 48 yield is correctlycalculated by GEF, while the contribution of the asymmetric component is underestimated. In view of the goodreproduction of the distributions of Z = 50 and higher, which fixes the shape of the heavy part of the asymmetriccomponent, the shape of the distribution of Z = 48 indicates the presence of a further-reaching tail of the asymmetriccomponent towards symmetry. This problem is already visible in the distributions from Z = 45 to Z = 47. However,the almost constant intensity of the right side-peak in these distributions from JEFF-3.3 is very difficult to reconcilewith the inherent regularities of the GEF model. The solution of this problem is not obvious. Our previous study[32] on fission-product yields from fission at higher excitation energies revealed the very same problem in the isotopicdistribution of Z = 49 for the electromagnetic-induced fission of U.In summary, the isotopic distributions with peak yields above 0.1% are fairly or well reproduced, except the problemnear symmetry. There is a need for re-considering the S3 fission channel and the competition between symmetric andasymmetric fission channels for Z = 48. Attempts for solving these problems have not yet been successful becauseGEF is not a direct fit to the fission yields. The inherent regularities of the GEF model and the reproduction ofother types of data, for example the mass-dependent prompt-neutron multiplicities, see ref. [89], impose additionalconstraints. Finally, one must always be aware that some evaluated yields might be erroneous, in particular in thelow-yield regions. U(n fast ,f )
In Figs. 83 to 88 that show the isotopic distributions of the reaction
U(n fast ,f), one observes about the samefeatures as found for
U(n th ,f). There is some additional erratic scattering, which may be attributed to the lowerquality of the evaluated data for this reaction. In addition, there are some indications for a slight systematic shift ofthe isotopic distributions from GEF towards the neutron-rich side in the light group and to the neutron-deficient sidein the heavy group. This might indicate an underestimated charge polarization or an overestimated amount of energysorting at scission. 61 X APPENDIX
Pu(n th ,f ) In the isotopic distributions of the reaction
Pu(n th ,f) shown in Figs. 89 to 94, the distributions with peakyields above 1% are at least fairly well reproduced, except the problems near symmetry. One observes an increasederratic scattering and larger error bars in the evaluated data than in the uranium cases discussed above. Most of thediscrepancies between the evaluation and the GEF results are not systematic. The problem found for the uraniumcases in the asymmetric wings does not appear clearly for Pu(n th ,f), except the shift to the neutron-deficient side inthe heavy wing. The problem at the transition from the symmetric component to the heavy asymmetric component,here appearing at Z = 47 and Z = 48, is again clearly visible.62 X APPENDIX
FIG. 77. Isotopic distributions of
U(n th ,f) fission-product yields for different elements, comparison of JEFF-3.3 (black symbolsand error bars) and GEF (magenta symbols), linear scale. The mean mass values are given in the appropriate color. X APPENDIX
FIG. 78. Isotopic distributions of
U(n th ,f) fission-product yields, comparison of JEFF-3.3 and GEF, linear scale. X APPENDIX
FIG. 79. Isotopic distributions of
U(n th ,f) fission-product yields, comparison of JEFF-3.3 and GEF, linear scale. X APPENDIX
FIG. 80. Isotopic distributions of
U(n th ,f) fission-product yields, comparison of JEFF-3.3 and GEF, logarithmic scale. X APPENDIX
FIG. 81. Isotopic distributions of
U(n th ,f) fission-product yields, comparison of JEFF-3.3 and GEF, logarithmic scale. X APPENDIX
FIG. 82. Isotopic distributions of
U(n th ,f) fission-product yields, comparison of JEFF-3.3 and GEF, logarithmic scale. X APPENDIX
FIG. 83. Isotopic distributions of
U(n fast ,f) fission-product yields, comparison of JEFF-3.3 and GEF, linear scale. X APPENDIX
FIG. 84. Isotopic distributions of
U(n fast ,f) fission-product yields, comparison of JEFF-3.3 and GEF, linear scale. X APPENDIX
FIG. 85. Isotopic distributions of
U(n fast ,f) fission-product yields, comparison of JEFF-3.3 and GEF, linear scale. X APPENDIX
FIG. 86. Isotopic distributions of
U(n fast ,f) fission-product yields, comparison of JEFF-3.3 and GEF, logarithmic scale. X APPENDIX
FIG. 87. Isotopic distributions of
U(n fast ,f) fission-product yields, comparison of JEFF-3.3 and GEF, logarithmic scale. X APPENDIX
FIG. 88. Isotopic distributions of
U(n fast ,f) fission-product yields, comparison of JEFF-3.3 and GEF, logarithmic scale. X APPENDIX
FIG. 89. Isotopic distributions of
Pu(n th ,f) fission-product yields, comparison of JEFF-3.3 and GEF, linear scale. X APPENDIX
FIG. 90. Isotopic distributions of
Pu(n th ,f) fission-product yields, comparison of JEFF-3.3 and GEF, linear scale. X APPENDIX
FIG. 91. Isotopic distributions of
Pu(n th ,f) fission-product yields, comparison of JEFF-3.3 and GEF, linear scale. X APPENDIX
FIG. 92. Isotopic distributions of
Pu(n th ,f) fission-product yields, comparison of JEFF-3.3 and GEF, logarithmic scale. X APPENDIX
FIG. 93. Isotopic distributions of
Pu(n th ,f) fission-product yields, comparison of JEFF-3.3 and GEF, logarithmic scale. X APPENDIX
FIG. 94. Isotopic distributions of
Pu(n th ,f) fission-product yields, comparison of JEFF-3.3 and GEF, logarithmic scale. X APPENDIX
FIG. 95. Isotopic distributions of
Pu(n th ,f) fission-product yields, comparison of JEFF-3.3 and GEF, linear scale. X APPENDIX
FIG. 96. Isotopic distributions of
Pu(n th ,f) fission-product yields, comparison of JEFF-3.3 and GEF, linear scale. X APPENDIX
FIG. 97. Isotopic distributions of
Pu(n th ,f) fission-product yields, comparison of JEFF-3.3 and GEF, linear scale. X APPENDIX
FIG. 98. Isotopic distributions of
Pu(n th ,f) fission-product yields, comparison of JEFF-3.3 and GEF, logarithmic scale. X APPENDIX
FIG. 99. Isotopic distributions of
Pu(n th ,f) fission-product yields, comparison of JEFF-3.3 and GEF, logarithmic scale. X APPENDIX
FIG. 100. Isotopic distributions of
Pu(n th ,f) fission-product yields, comparison of JEFF-3.3 and GEF, logarithmic scale. X APPENDIX
Pu(n th ,f ) The isotopic distributions of
Pu(n th ,f) fission-product yields in Figs. 95 to 100 show strong discrepancies betweenthe evaluation and the GEF results. Most of these discrepancies are related to the serious problems found in the massyields of this system, see Figs. 101 and 102 of the main document. These problems do not allow to make a moredetailed discussion of the isotopic distributions. Summary
The comparison of the isotopic distributions from the JEFF-3.3 evaluation with the results from the GEF codereveals a rather good, often almost perfect agreement for the yields of the elements with values above 1%. Thiscomparison also reveals the exceptionally good quality of the empirical data for the system
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