Energy Procedia 71 ( 2015 ) 205 – 212

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1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).Selection and peer-review under responsibility of the Tokyo Institute of Technologydoi: 10.1016/j.egypro.2014.11.871

A comprehensive approach to estimate delayed-neutron data ofactinides and minor-actinides

Satoshi Chibaa,∗, Katsuhisa Nishiob, Yoshihiro Aritomoa, Hiroyuki Kourab, OsamuIwamotoc, Teruhiko Kugoc

aResearch Laboratory for Nuclear Reactors, Tokyo Institute of Technology, 2-12-1, Ookayama, Meguro-ku, Tokyo 152-8550 JapanbAdvanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan

cNuclear Science and Engineering Directorate, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan

Abstract

A project is described on a comprehensive approach to improve accuracy of delayed-neutron data of actinides and minoractinides by the summation calculations. This project consists of 1) measurement of fission fragment mass distribution(FFMD) of nuclei for which direct measurements using neutrons are not practical, 2) estimation of independent fissionyields by developing a dynamical model of fission, 3) improvement of a β-decay theory for better reproductions of decaycharacteristics of fission fragments, 4) nuclear data evaluation based on the above activities and summation calculationsof decay-heat and delayed neutron data and 5) benchmark by using reactor data. Through these activities, understandingof the basic fission process will be advanced as well.

c© 2014 Published by Elsevier Ltd.Selection and peer-review under responsibility of the Tokyo Institute of Technology.

Keywords: Nuclear data, delayed-neutron, surrogate method, Langevin theory, Gross theory of β-decay, reactorbenchmark

1. Introduction

Nuclear fission is the fundamental physical process underlying nuclear energy systems, one of the im-portant sources of energy. Application of the fission to technology has been progressed quite rapidly shortlyafter discovery of the fission. In contrast, understanding of the basic fission process itself has advancedrelatively slowly. For example, our knowledge on the origin of the mass-asymmetric division of fissionfragments, prompt and delayed neutrons and their energy spectra, from neutron impact on 233U, 235U and239Pu is still in a qualitative (or phenomenological) level. Needless to say, the situation is much worse forminor actinides for which direct measurement is difficult to be performed due to difficulties in preparingtarget materials.

Delayed neutron data is one of the key information to evaluate kinetic behavior of nuclear reactorsduring normal operation. Furthermore, reactivity ρ of nuclear reactors in transient status and that of other

∗Corresponding AuthorEmail address: chiba.satoshi@nr.titech.ac.jp (Satoshi Chiba)

© 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).Selection and peer-review under responsibility of the Tokyo Institute of Technology

206 Satoshi Chiba et al. / Energy Procedia 71 ( 2015 ) 205 – 212

subcritical nuclear facilities such as accelerator-driven system for nuclear-waste transmutation may be givenby using the reactor period T (a measurable quantity) as

ρ =�

T + �+

TT + �

6∑i=1

βi,e f f

1 + λiT(1)

where � denotes mean lifetime of prompt neutrons, βi,e f f the effective delayed-neutron fraction of group i,and λi its decay constant. That is, an observable (T ) and the reactivity (one of the most important designcriteria) is connected through the delayed neutron data. Therefore, if the delayed-neutron data is uncertain,the reactivity determined by this relation is uncertain as well.

Delayed neutrons appear after β-decay of fission fragments which are populated mostly as neutron-richnuclei. Estimation of the delayed-neutron data requires, hence, a comprehensive knowledge on the fission ofrelevant nuclei, namely, how the fission fragments are populated in nuclear chart and how they decay towardstable nuclei if not measured directly as was done by Keepin[15, 16]. They are also related closely to theproblems of decay heat and emission of reactor antineutrinos, the latter attains strong recent interest since itis related to the fundamental problem such as neutrino oscillation and possibility of reactor monitoring fornon-proliferation of nuclear materials. Therefore, it is desirable to understand these problems systematicallyin a process of understanding the physical phenomena related to the nuclear fission. Brady and England[4]has made a first and pioneering attempt toward this direction, and carried out a summation calculation.However, there are still many open problems left in this field because the physics of fission and neutron-rich nuclei are complicated and actually are matters of the front-edge nuclear physics. For example, if wecompare the reactivities calculated by using 6-group delayed neutron data measured by Keepin et al.[15]and those calculated by Brady and England for major actinide like 235U, they disagree about 10% for awide range of the reactor period. Therefore, many efforts must be done in order to make more accurate themicro-physics information, i.e., fission fragment yield and their decay data, necessary for the summationcalculation of delayed neutrons to a practical level.

In this work, we introduce new experimental techniques and theoretical frameworks to make more ac-curate the summation calculation of delayed neutron data. Existing data for the major actinides are alsoanalyzed simultaneously. The latter will serve as a benchmark of the present approach.

2. Method

2.1. Overall framework

We will conduct the following comprehensive and systematic researches to improve our knowledge onthe delayed neutrons as collaboration between Tokyo Tech. and JAEA as a 4-year project supported byMEXT. Firstly, mass distribution of fission fragments (MDFF) will be measured by the surrogate method.It will yield excitation-energy dependence of MDFF both for major and minor actinides, the latter are hardto be obtained by other methods. Secondly, independent fission yield of major and minor actinides will beestimated by a multi-dimensional Langevin theory which is tuned to reproduce the MDFF data obtainedby the surrogate method. Thirdly, gross theory of β-decay will be extended to reproduce available up-to-date data for the half lives of β-decay, spectra of β-rays and γ-rays including recent TAGS (Total AbsorptionGamma-ray Spectrometer) data and delayed neutron emission probabilities of relevant nuclei. The improvedgross theory will be used to estimate the decay heat, delayed-neutron emission and emission of antineutrinos(including their spectra). Furthermore, a statistical decay model based on the Hauser-Feshbach theory[12]will be employed to estimate prompt neutron emission which modifies the independent fission yields aswell as the delayed-neutron emission probability and spectra of delayed neutrons. Finally, a temporaryevaluated nuclear data library will be generated and summation calculation of the decay heat and delayed-neutron related quantities will be carried out, which will be tested against integral data. This informationwill then be used to further update various components emerging in the former stages of this project until asatisfactory agreement is obtained. The flow of the present work is schematically illustrated in Fig. 1.

Major items of the present project will be described in more details in the followings.

Satoshi Chiba et al. / Energy Procedia 71 ( 2015 ) 205 – 212 207

Fig. 1. Schematic illustration of the present project showing relationship of different subtopics. 1. Measurement of MDFF of actinidesand minor-actinides by the surrogate method, 2. Calculation of the independent fission yield by a multi-dimensional Langevin modelapproach, 3. Improvement of the gross-theory of β-decay for better prediction of the delayed-neutron emission probabilities of neutron-rich fission fragments, and 4. Summation calculation based on a constructed nuclear data for validation in terms of decay heat, ν̄d andβeff , and prediction of spectra of reactor antineutrinos.

2.2. Surrogate method

Neutron-induced reaction data for unstable and/or rare nuclei may be obtained at high-intensity neutron-source facilities such as n-TOF [18] and ANNRI at J-PARC [11]. However, difficulty of preparing targetmaterials makes it difficult even at these facilities for many target nuclei. An alternative is to use the sur-rogate method, where (multi-)nucleon transfer reactions are used to populate the same compound nuclei asthe desired neutron-induced reactions to determine the decay branching ratio to various channels. Such atechnique was pioneered to determine fission barriers [5, 3, 10] and was later extended to determine neutron-induced fission and capture cross sections (see a thorough review by Escher et al.[9]). Validity of this methodis also discussed intensively in Refs.[6, 7, 1]. In this project, we work primarily with the surrogate methodusing heavy-ion projectiles to determine mass distribution of fission fragments from minor actinides.

Experimental apparatus was developed and located at Tandem accelerator facility of JAEA Tokai site. Itconsists of a multi-wire proportional counter (MWPC) and a ΔE-E counter made of Si detectors as shownin Fig. 2. Both were contained in a specially designed vacuum chamber. We have performed experimentsimpinging a beam of 18O on 238U target. Typical beam energy was 157.5 MeV, beam current was 0.5 particlenA, and target thickness was about 44.3 μg/cm2. Advantage of employing a heavy-ion beam such as 18Oin the surrogate method is demonstrated[19]. Many kinds of nucleon transfer reactions took place, andwide variety of different excited nuclei were populated as a result. The populated nuclei were identified bydetecting outgoing particle species and their energies by the ΔE-E counter. Fission fragments were detectedby 4 MWPCs surrounding the target in coincidence with each outgoing particle. Therefore, we could give acorrespondence between the fission fragments and the decaying nuclei which populated them.

The fission events following nucleon transfer were discriminated against those from the full momentum-transfer (fusion-fission) events by using kinematical conditions. Difference in the flight-time of the 2 fissionfragments were converted to mass ratio of them, and the MDFF were deduced for each of the excited

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fissioning nuclei populated by the surrogate method as a function of excitation energies. For the particularcase of 18O on 238U reaction, the stripping reactions took place stronger than the pickup ones. Therefore, wecould populate compound nuclei having more neutrons and protons than the target nucleus. In this project,we are going to employ targets of 232Th, 238U, 237Np and 248Cm. Therefore, we expect to populate a widevariety of compound nuclei as the fissioning system as shown in Fig. 3

Fig. 2. Major components of the experimental setup in the surrogate method: a vacuum chamber, a MWPC (Multi-wire ProportionalCounter) and a Si ΔE-E detector.

2.3. Multi-dimensional Langevin Model Calculation

A dynamical model of nuclear fission is being developed based on the fluctuation-dissipation theoremformulated as the Langevin equations on a potential energy surface calculated by the 2-center shell model(Aritomo 2013). The shell effect was taken into account by the Strutinski’s method[20]. The Langevinequations to describe time evolution of collective variables qi expressing nuclear shape during the fission(i=1, 2,3 : center distance between 2 fragments, their deformation and mass asymmetry) and their conjugatemomenta pi are given as

dqi

dt=(m−1)

i jp j,

dpi

dt= −∂V∂qi− 1

2∂

∂qi

(m−1)

jkp j pk − γi j

(m−1)

jkpk + gi jR j(t),

where summation over repeated indices is assumed. Here, V denotes the potential energy surface calculatedby the 2-center shell model, R(t) being the random force having the nature of white noise (Markov process),gi j its strength. The transport coefficients mi j (mass tensor) and γi j (friction coefficients) were calculated bya semiclassical manner with hydrodynamical and wall-and-window models, respectively. The gi j and γi j arerelated to each other by the Einstein relation γi jT = gik ·g jk, where T denotes the nuclear temperature relatedwith the intrinsic energy of the fissioning nuclei. Nucleon transfer between the fragments is determined bya diffusion-type equation with a drift term for neutron and proton separately. In this way we can determinethe isotopic distribution (the primary yield before emission of prompt neutrons) of fission fragments as wellas the mass distribution to be compared with the results obtained by the surrogate method.

Satoshi Chiba et al. / Energy Procedia 71 ( 2015 ) 205 – 212 209

Fig. 3. Expected compound nuclei to be populated by surrogate reactions with 18O beam on 232Th, 238U, 237Np and 248Cm targets(circles) are denoted by diamonds.

Starting from the ground state, the Langevin trajectories are calculated for many events. The fissionevents are determined in our model calculation by tracing the time evolution of the trajectories in the de-formation space. Fission from a compound nucleus is defined as the case that a trajectory overcomes thescission point on the potential energy surface at which we can determine the mass and isotopic distributionof the fission fragments (before emission of prompt neutrons from the fragments). The pre-scission neutronemission is taken into account in the Langevin calculation based on the statistical model.

Dependence of the calculated results on the model parameters such as the friction coefficients is inves-tigated. It was found that overall strength of the friction coefficients had little influence on the final MDFF.The formulation, sensitivity to model parameters, and our first results were published in Ref. [2].

2.4. Gross theory of β-decay

The β-decay of fission fragments are treated by the gross theory[24, 17]. The gross theory is constructedunder a consideration that in the quantum mechanics the sum (and the energy-weighted sum) of strengthsof the transition from the initial state to various final states should satisfy a constraint or a simple functionalform deduced by the physical considerations. Details of the discrete level structure of single-particle statesare replaced with a smooth function except for some irregularities owing to the paring effects, and thestrength functions of the decay are given by analytical functions. The nuclear level densities are simplytreated by the Fermi-gas model. The transition probabilities are given for the allowed transition as the Fermiand Gamow-Teller transition as well as for the 1st-forbidden transitions[25].

The delayed neutron emission probability is calculated by integrating from threshold energy of neutronemission to the ground-state energy of the parent nucleus as[26]

Pn =Cλβ

∫ 0

−Qβ+S n

|M(E)|2 f (Z,−E)Γn

Γn + ΓγdE (2)

where C is a constant related to the coupling constant of the β decay, M the strength function, f the integratedFermi function, Γx being average decay width for neutron (x = n) or γ (x = γ) channel. The symbols λβ,Qβ and S n denote the β-decay transition rate, Q-value of the β-decay and neutron separation energy of thedaughter nucleus, respectively. The decay with Γ is introduced to express competition between neutronemission and gamma decay from excited states, which can be calculated based on the statistical model.

The model has been improved further to take account of some of the nuclear structure effects[22, 23].Parameters used to specify the strength functions are adjusted to reproduce global feature of the β-decay inthe early works. In this project, however, we reconsider the shapes of the strength function and treat themmainly for the delayed neutrons because the trend of Pn goes smoothly along the change of the strength

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functions. Then the total half-lives are treated by considering the precise nuclear structure due to sensitivitiesof the half-lives to the nuclear structure.

It is also an important aim of this project to populate a database for energy spectra of antineutrinosemitted from the fission fragments so that we can calculate the strength and energy spectra of reactor an-tineutrinos.

2.5. Update of data library and benchmarkThe FFMD data obtained by the surrogate method will be used to improve the Langevin-model cal-

culation, which will yield the independent yield data after correction of emission of the prompt neutronsfrom the fission fragments. These data will be employed to update the JENDL Fission Product Yield DataFile[14], a part of JENDL-4[21, 13] by a Bayesian-type statistical inference. The neutron emission proba-bilities Pn calculated by the Gross Theory will be used to update the JENDL Fission Product Decay DataLibrary in a similar manner. Then, a new prototype nuclear data library will be generated, and it will bebenchmarked against various quantities such as decay heat, Keepin-type delayed-neutron data and βe f f ofcritical assemblies and nuclear reactors. If inconsistencies are detected, we will feedback that informationto the prototype library, and new update procedure will be carried out.

3. Results and discussions

A part of the MDFF data measured by the surrogate method is displayed in Fig. 4, where yields ofvarious mass number of the fission fragment (horizontal axes) are plotted as a function of excitation energyof the fissioning system (vertical axes). These excitation-energy dependent MDFF data will be employed todevelop a dynamical model of nuclear fission in terms of the Langevin model.

Fig. 4. A part of the preliminary results of MDFF obtained by the surrogate method by the 18O + 238U reaction.

Figure 5 compares measured and calculated MDFF data from 236U at excitation energy of 20 MeV.The present calculation (the histogram) is favorably compared with evaluated data. The discrepancy for thedistribution at the peak corresponding to the light fragments can be attributable to the fact that our results arefor the primary fission fragments, while the evaluated data are given as the independent fission yield (afteremission of prompt neutrons).

Some efforts are still needed to advance accuracy of this model. Firstly, the Langevin calculation mustbe improved to include 4 collective variables. The 4-th parameter corresponds to difference of deformationsof the 2 fission fragments. Furthermore, the effect of the emission of the prompt neutrons from the fissionfragments must be taken into consideration. It will be corrected in our calculation by considering a decayof the excited fragments by the Hauser-Feshbach theory[12] in a future work of our project. Then, wecan calculate the independent fission yield, which must be verified by a comparison with experimental dataobtained by the surrogate method. Once the model is verified, we are able to apply it to calculate theindependent fission yield of minor actinides for which no experimental data is available to calculate thedelayed-neutron data.

Satoshi Chiba et al. / Energy Procedia 71 ( 2015 ) 205 – 212 211

Fig. 5. Mass distribution of fission fragments of 236U at excitation energy of 20 MeV (a fissioning system equivalent to that of 14 MeVneutrons on 235U). The dots are from evaluated nuclear data JENDL-4[13] representing experimental information, while the histogramshows the result of present calculation[2].

4. Conclusion

Estimation of the delayed-neutron data requires a comprehensive knowledge on the fission of relevantnuclei, namely, how the fission fragments are populated in nuclear chart (independent yield) and how theseneutron-rich nuclei decay toward stable ones. They are also related closely to the problems of decay heatand emission of reactor antineutrinos, the latter attains strong recent interest since it is related to the reactor-neutrino oscillation and possibility of reactor monitoring for non-proliferation of nuclear materials.

In our approach, we will conduct the following comprehensive researches systematically to improve ourknowledge on the delayed neutrons:

1. Measurement of fission fragment mass distribution (FFMD) data by the surrogate method with heavy-ion projectiles. It will yield excitation energy dependence of FFMD and data for minor actinideswhich are hard to be obtained by other methods.

2. Estimation of the independent fission yield by a multi-dimensional Langevin model calculation whichis tuned to reproduce the FFMD data obtained in item 1.

3. Gross theory of β-decay will be extended to reproduce available up-to-date data for the half lives ofβ-decay, spectra of β-rays and γ-rays, and delayed neutron emission probabilities of relevant nuclei.Then, it will be used to estimate the decay heat, delayed-neutron emission and emission of antineutri-nos (including their spectra) of nuclei for which no data are available.

After these researches yielded some results, the following will be done successively:

4. A statistical decay model based on the Hauser-Feshbach theory will be fully employed in conjunctionwith items 2. and 3. In item 2., it will be used to estimate prompt neutron emission which modifiesthe independent fission yields. In item 3., the statistical decay model estimates the delayed-neutronemission probability and spectra of delayed neutrons.

5. A temporary evaluated nuclear data library will be generated and tested against integral data. Thisinformation will then be used to further update various components emerging from items 2. to 4 untila satisfactory agreement is obtained.

Such a comprehensive study will advance our knowledge on the fundamental properties of the fissionprocess and the fission products.

212 Satoshi Chiba et al. / Energy Procedia 71 ( 2015 ) 205 – 212

Acknowledgments

Present study is the results of “Comprehensive study of delayed-neutron yields for accurate evaluation ofkinetics of high-burn up reactors” entrusted to Tokyo Institute of Technology by the Ministry of Education,Culture, Sports, Science and Technology of Japan (MEXT).

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