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随着第四代反应堆以及先进核能利用系统的发展, 对中子核数据提出了高精度、多核素、宽能区的新要求. 目前, 中国核数据评价库(CENDL库)中相关核裂变的数据较缺失, 不足以满足当前核能发展的需求. 因此, 建立面向中子核数据需求的可靠计算方法和工具变得极为重要. 本文基于Monte-Carlo方法建立了裂变碎片质量动能计算模型, 研究了中低能中子诱发232Th(n,f)反应发射中子前裂变碎片的分布特性. 对于裂变碎片质量分布, 本模型计算结果与实验值最大偏差约1%, 与GEF, TALYS程序计算结果(与实验值最大偏差约2%)相比具有一定优势. 对于发射中子前裂变碎片动能分布, 本模型计算结果与实验数据一致. 结果表明, 所发展的计算模型能够较好地预测232Th(n,f)反应发射中子前裂变碎片数据, 为中子诱发锕系核裂变反应计算提供一种新思路.The development of fourth-generation reactors and advanced nuclear energy systems require high-precision, multi-nuclide, and wide-energy-area neutron nuclear data. However, the current nuclear energy-related nuclear fission data in the China Nuclear Data Evaluation Library (CENDL library) are incomplete and cannot meet the current need. It is extremely important to establish the reliable calculation methods and tools for the neutron nuclear data. Based on the Monte-Carlo method, a model for calculating the pre-neutron fission fragment is established in this work. The mass and kinetic energy distribution of 232Th(n,f) reaction at the medium- and low- incident neutron energy are studied. The calculations of the mass distribution with the different values of incident energy are compared with the experimental results. The maximum deviation of this work from the experimental data is ~1%, which is advantageous compared with the GEF and TALYS code (maximum deviation from the experimental value is ~2%). The calculation of the pre-neutron fission fragment kinetic energy also shows good agreement with experimental result. The results indicate that this model can well describe and predict the characteristics of pre-neutron fission fragment for 232Th(n,f) reaction at the medium- and low- incident neutron energy. It also provides a new idea for calculating the neutron-induced actinide fission reactions.
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Keywords:
- pre-neutron emission fission fragments /
- mass distribution /
- total kinetic energy distribution /
- Monte-Carlo method
[1] Talou P, Becker B, Kawano T, Chadwick M B, Danon Y 2011 Phys. Rev. C 83 1509
[2] 张竞上 2003 现代物理知识 01 24
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Li G C 2017 Ph. D. Dissertation (Shanghai: Shanghai Institute of Applied Physics, Chinese Academy of Sciences) (in Chinese)
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Google Scholar
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Google Scholar
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Hao Y W, Dong G X, Wang X B 2019 Scientia Sinica Physica, Mechanica & Astronomica 49 122001
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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图 1 Geant4几何模型示意图. 灰色区域代表锕系核素样品(Sample), 黄色区域代表衬底(Backing). 面向入射中子一侧为样品侧(Sample side), 远离入射中子一侧为衬底侧(Backing side). FF1和FF2分别代表一对互补裂变碎片, 并且它们穿出靶的角度分别为θ1和θ2
Fig. 1. Schematic illustration of the Geant4 geometric model. The gray layer is the fissile sample of the actinide target, while the yellow one is the backing support for the sample. The sample side faced the impinging neutrons. FF1 and FF2 respectively denote the fragments emitted from the different sides. θ1 and θ2 are the angles of the fragment axis relative to the axial direction of the incoming neutron.
图 2 发射中子后裂变碎片初始动能
$ {E^{{\text{post}}}} $ 与碎片出射方向相对中子入射方向夹角的余弦值$ \cos \theta $ 的关系 (a) 碎片从样品侧穿出时计算结果; (b) 碎片从衬底侧穿出时计算结果Fig. 2.
$ \cos \theta $ versus post-neutron emission kinetic energy$ {E^{{\text{post}}}} $ distribution: (a) The case of the fission fragments from sample side; (b) in the case of the fission fragments from backing side.
图 3 232Th(n, f)反应发射中子后TKE分布 (a)中子能量为3 MeV; (b)中子能量为6 MeV; (c)中子能量为10 MeV. 黑线为实验数据[13]; 红线为本文计算数据
Fig. 3. Post-neutron emission TKE distribution for 232Th(n, f) reaction: (a) En = 3 MeV; (b) En = 6 MeV; (c) En = 10 MeV. The black line denotes experimental data [13]. The red line denotes the calculated result from this work.
图 4 232Th(n, f)反应发射中子后平均总动能
$ {\overline {{\text{TKE}}} _{{\text{post}}}} $ 随入射中子能量的变化情况. 红点为本文计算数据, 其他颜色点为实验数据[13,35-37]Fig. 4. Relationship between the incident neutron energy and
$ {\overline {{\text{TKE}}} _{{\text{post}}}} $ for 232Th(n, f) reaction. The red dots denote the calculated results from this work. The dots with other colors denote the experimental data 13,35-37].
图 5 不同入射中子能量下, 232Th(n, f)反应中子多重性
$ \overline \nu (m) $ 的计算结果Fig. 5. Calculation of neutron multiplicity distribution
$ \overline \nu (m) $ for 232Th(n, f) reaction with the different incident neutron energies.
图 6 发射中子前裂变碎片质量、总动能分布计算流程图
Fig. 6. Program flow chart for the calculation of the pre-neutron fission fragment mass and TKE distribution.
图 7 232Th(n, f)反应发射中子前裂变碎片质量分布 (a)中子能量为1.6 MeV; (b)中子能量为3 MeV; (c)中子能量为6 MeV; (d)中子能量为10 MeV. 黑色实心点代表实验结果[14,15], 红线为本工作结果, 蓝线为GEF结果, 绿线为TALYS结果
Fig. 7. Calculation of the pre-neutron mass distribution for 232Th(n, f) reaction: (a) En = 1.6 MeV; (b) En = 3 MeV; (c) En = 6 MeV; (d) En = 10 MeV. The black dots line is experimental data [14,15]. The red line is the calculated data from this work, while the blue one is from the GEF code and the green one is from the TALYS code.
图 8 232Th(n, f)反应质量分布计算与实验结果偏差分析 (a)中子能量为1.6 MeV; (b)中子能量为3 MeV; (c)中子能量为6 MeV; (d)中子能量为10 MeV. 红线为本工作结果, 蓝线为GEF结果, 绿线为TALYS结果
Fig. 8. Difference of the mass distribution between calculation and experimental data for 232Th(n, f) reaction: (a) En = 1.6 MeV; (b) En = 3 MeV; (c) En = 6 MeV; (d) En = 10 MeV. The red line is the calculated data from this work, while the blue one is from the GEF code and the green one is from the TALYS code.
图 9 发射中子前裂变碎片质量-TKE的二维分布 (a)中子能量为1.6 MeV; (b)中子能量为3 MeV; (c)中子能量为6 MeV; (d)中子能量为10 MeV. 黑点表示碎片质量与平均总动能
$ {\overline {{\text{TKE}}} _{{\text{pre}}}}({m^{{\text{pre}}}}) $ 关系. 图例中颜色标度反映了事件数目Fig. 9. Two-dimension distribution of pre-neutron mass versus TKE: (a) En = 1.6 MeV; (b) En = 3 MeV; (c) En = 6 MeV; (d) En = 10 MeV. The black dots denote
$ {\overline {{\text{TKE}}} _{{\text{pre}}}}({m^{{\text{pre}}}}) $ , the relationship between pre-neutron mass and average TKE. The color scale refers to the number of events.
图 10 232Th(n, f)反应发射中子前平均总动能
$ {\overline {{\text{TKE}}} _{{\text{pre}}}} $ 随入射中子能量变化情况. 红点为本文计算数据, 其他颜色点为实验数据[13,35,43,44]Fig. 10. Relationship between the incident neutron energy and
$ {\overline {{\text{TKE}}} _{{\text{pre}}}} $ for 232Th(n, f) reaction. The red dots denote the calculated results from this work. The dots with other colors denote the experimental data 13,35,43,44]. -
[1] Talou P, Becker B, Kawano T, Chadwick M B, Danon Y 2011 Phys. Rev. C 83 1509
[2] 张竞上 2003 现代物理知识 01 24
Zhang J S 2003 Mod. Phys. 01 24
[3] Forrest R A 2011 Energy Procedia 7 540
Google Scholar
[4] Möller P, Sierk A J 2003 Nature 422 485
[5] Al-Adili A, Hambsch F J, Pomp S, Oberstedt S, Vidali M 2016 Phys. Rev. C 93 34603
Google Scholar
[6] Salvador-Castineira P, Brys T, Eykens R, Hambsch F-J, Göök A, Moens A, Oberstedt S, Sibbens G, Vanleeuw D, Vidali M 2015 Phys. Rev. C 92 014620
Google Scholar
[7] Meierbachtol K, Tovesson F, Duke D L, Geppert-Kleinrath V, Manning B, Meharchand R, Mosby S, Shields D 2016 Phys. Rev. C 94 034611
Google Scholar
[8] 蔡翔舟, 戴志敏, 徐洪杰 2016 物理 45 578
Google Scholar
Cai X Z, Dai Z M, Xu H J 2016 Physics 45 578
Google Scholar
[9] Crasta R, Naik H, Suryanarayana S V, Shivashankar B S, Mulik V K, Prajapati P M, Sanjeev G, Sharma S C, Bhagwat P V, Mohanty A K, Ganesan S, Goswami A 2012 Ann. Nucl. Energy 47 160
Google Scholar
[10] 李光超 2017 博士学位论文 (上海: 中国科学院上海应用物理研究所)
Li G C 2017 Ph. D. Dissertation (Shanghai: Shanghai Institute of Applied Physics, Chinese Academy of Sciences) (in Chinese)
[11] Trochon J, Yehia H A, Brisard F, Pranal Y 1979 Nucl. Phys. A 318 63
Google Scholar
[12] Naik H, Mukherji S, Suryanarayana S V, Jagadeesan K C, Thakare S V, Sharma S C 2016 Nucl. Phys. A 952 100
Google Scholar
[13] King J, Yanez R, Loveland W, Barrett J S, Oscar B, Fotiades N, Tovesson F, Lee H Y 2017 Eur. Phys. J. A 53 238
Google Scholar
[14] Sergachev A I, Vorob'Eva V G, Kuz'Minov B D, Mikhailov V B, Tarasko M Z 1968 Yadern. Fiz. 7 778
[15] Ryzhov I V, Yavshits S G, Tutin G A, Kovalev N V, Saulski A V, Kudryashev N A 2011 Phys. Rev. C 83 054603
Google Scholar
[16] 葛智刚, 陈永静 2015 科学通报 60 3087
Google Scholar
Ge Z G, Chen Y J 2015 Chin. Sci. bull. 60 3087
Google Scholar
[17] Schmidt K H, Jurado B, Amouroux C 2016 Nucl. Data Sheets 131 107
Google Scholar
[18] Koning A J, Hilaire S, Duijvestijn M C 2007 Proceedings of the International Conference on Nuclear Data for Science and Technology Nice, France, April 22–27, 2007 pp1–214
[19] 郝艺伟, 董国香, 王小保 2019 中国科学: 物理学 力学 天文学 49 122001
Hao Y W, Dong G X, Wang X B 2019 Scientia Sinica Physica, Mechanica & Astronomica 49 122001
[20] Brosa U 1985 Phys. Rev. C 32 1438
Google Scholar
[21] Brosa U, Grossmann S, Muller A, Becker E 1989 Nucl. Phys. A 502 423c
Google Scholar
[22] Hambsch F J, Vivès F, Siegler P, Oberstedt S 2000 Nucl. Phys. A 679 3
Google Scholar
[23] Agostinelli S, Allison J, Amako K, et al. 2003 Nucl. Instrum. Methods A 506 250
Google Scholar
[24] Mosby S, Tovesson F, Couture A, Duke D L, et al. 2014 Nucl. Instrum. Methods A 757 75
Google Scholar
[25] Vivès F, Hambsch F J, Bax H, Oberstedt S 2000 Nucl. Phys. A 662 63
Google Scholar
[26] Zeynalova O V, Zeynalov S, Hambsch F J, Oberstedt S, Fabry I 2010 Bull. Russ. Acad. Sci. Phys. 74 800
Google Scholar
[27] Chadwick M B, Herman M, Obložinský P, et al. 2011 Nucl. Data Sheets 112 2887
Google Scholar
[28] Liu C Q, Hu Z M, Hu Z J, et al. 2021 J. Instrum. 16 P07038
Google Scholar
[29] Wang D, Zhang C, Zhang J H 2015 Radiat. Meas. 73 46
Google Scholar
[30] Liu C Q, Wei Z, Han C, et al. 2019 Chin. Phys. C 43 064001
Google Scholar
[31] Wei Z, Yao Z E, Lan C L, et al. 2015 J Radioanal. Nucl. Chem. 305 455
Google Scholar
[32] Lan C L, Peng M, Zhang Y, Wei Z, Yao Z E, Xie B L 2017 Nucl. Sci. Technol. 28 8
Google Scholar
[33] Duke D L, Tovesson F, Laptev A B, Mosby S 2016 Phys. Rev. C 94 054604
Google Scholar
[34] Al-Adili A, Hambsch F J, Oberstedt S, Pomp S, Zeynalov S H 2010 Nucl. Instrum. Methods A 624 684
Google Scholar
[35] Higgins D, Greife U, Tovesson F, Manning B, Mayorov D, Mosby S, Schmitt K 2020 Phys. Rev. C 101 014601
Google Scholar
[36] Goverdovsky A A, Kuzminov B D, Mitrofanov V F, Sergachev A I 1997 Phys. At. Nucl. 60 1787
[37] Trochon J, Yehia H A, Brisard F, Pranal Y 1979 Nuclear Physics A 318 63
[38] Stanley L, Whetstone J 1958 Phys. Rev. 114 581
[39] Albertsson M, Carlsson B G, Døssing T, Möller P, Randrup J, Åberg S 2021 Phys. Rev. C 103 014609
Google Scholar
[40] Chen Y J, Liu T J 2011 Chin. Phys. C 35 344
Google Scholar
[41] Göök A, Hambscha F J, Oberstedta S, Vidalia M 2015 Physics Procedia 64 190
Google Scholar
[42] Schmidt K H, Jurado B 2010 Phys. Rev. Lett. 104 242501
[43] Dyachenko N P, Kuzminov B D, Mitrofanov V F, Sergachev A I 1977 Yadern. Fiz. 26 691
[44] Lam S T, Yu L L, Fielding H W, Dawson W K, Neilson G C 1983 Phys. Rev. C 28 1212
Google Scholar
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