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本文利用三维格点空间相对论密度泛函理论, 在轴对称破缺, 反射对称破缺和$V_{4}$对称性破缺时, 计算了锕系原子核的势能曲线, 探索了所有四极和八极形变自由度对裂变内垒, 外垒和同核异能态的影响. 我们的计算结果表明: 反射对称性破缺能显著地降低外垒的高度, 轴对称性破缺能同时降低内垒和外垒的高度, $V_{4}$对称性破缺对内垒和外垒几乎没有影响, 同核异能态几乎不受对称性破缺的影响. 基于相对论密度泛函PC-PK11, 对同核异能态的能量经验值有轻微低估. 本文数据集可在
https://www.doi.org/10.57760/sciencedb.j00213.00229 中访问获取.-
关键词:
- 相对论密度泛函理论 /
- 三维格点空间 /
- 裂变位垒 /
- $V_{4}$对称性
Nuclear fission is a decay process by which a heavy nucleus splits into two or more lighter nuclei. It plays a crucial role in the synthesis of superheavy elements, the rapid neutron-capture process, nuclear energy application and so on. The fission barrier is an important property of heavy nuclei, because its height and width directly relate with the lifetime of heavy nuclei, and affect charge yield, mass yield, and kinetic energy of fission fragments. In our study, the potential energy curves of actinide nuclei are obtained from the relativistic density functional theory in 3D lattice when the axial symmetry, reflection symmetry and $V_4$ symmetry are broken in turn. The effects of all the quadrupole and octupole deformation degrees of freedom on the inner barrier, outer barrier, and the fission isomeric state are investigated. It is found that breaking the reflection symmetry can lower the outer fission barriers significantly, breaking the axial symmetry can lower both the inner and outer barriers, breaking the $V_4$ symmetry has little effect on the inner and outer barriers, and the fission isomeric state is almost unaffected by symmetry breaking. Based on the relativistic density functional PC-PK1 and monopole pairing interaction, our results well reproduce the empirical values of the inner and outer barriers extracted from experiments, and the energies of the fission isomeric states are slightly underestimated. All the data presented in this paper is openly available athttps://www.doi.org/10.57760/sciencedb.j00213.00229 .-
Keywords:
- relativistic density functional theory /
- 3D lattice space /
- fission barrier /
- $V_{4}$ symmetry
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图 1 $ Z=94 $的偶偶核中子对隙(蓝色空心方框)和实验上提取的中子经验对隙(黑色实心方框)随质量数的变化. $ N=146 $的偶偶核的质子对隙(红色空心圆)和实验上提取的质子经验对隙(黑色实心圆)随质量数的变化
Fig. 1. The neutron pairing gap calculated by 3DRDFT (blue open square) and extracted from experiments (black solid square) versus mass number for the even-even nuclei with $ Z = 94 $. The proton pairing gap calculated by 3DRDFT (red open circle) and extracted from experiments (black solid circle) versus mass number for the even-even nuclei with $ N = 146 $.
图 2 $ ^{240}{\rm{Pu}} $分别在保持轴对称和反射对称性(紫色点划线), 轴对称性(蓝色短划线), $ V_{4} $对称性(红色实线)时的势能曲线以及$ V_{4} $对称性破缺后在裂变内垒, 外垒和同核异能态附近的势能(绿色空心圆). 经验裂变内垒$ B_f^i $, 外垒$ B_f^o $, 和同核异能态$ E_{{\rm{iso}}} $的能量由黑色横线标记. 取$ ^{240}{\rm{Pu}} $的基态能量为$ 0 $
Fig. 2. The potential energy curve of $ ^{240}{\rm{Pu}} $ with axial symmetry and reflection symmetry (purple dot-dashed line), axial symmetry (blue dashed line), $ V_{4} $ symmetry (red solid line) and potential energy of $ ^{240}{\rm{Pu}} $ nearby inner barrier, outer barrier, isomeric state with $ V_{4} $ symmetry breaking (green open circle). The empirical inner barrier $ B_{f}^{i} $, outer barrier $ B_{f}^{o} $ and isomeric state $ E_{iso} $ is denoted by the black dash line. The energy is normalized with respect to the energy of the ground state.
表 1 在$ V_{4} $对称性破缺时, 7 个锕系原子核的裂变内垒, 外垒和同核异能态的能量经验值[75,76]$ \Delta E_{{\rm{Exp}}} $和基于3DRDFT计算的能量$ \Delta E_{{\rm{Theo}}} $, 四极形变$ \beta_{20} $, $ \beta_{22} $和八级形变$ \beta_{30} $, $ \beta_{31} $, $ \beta_{32} $, $ \beta_{33} $
Table 1. The energies extracted from experiments $ \Delta E_{{\rm{Exp}}} $ and the energies $ \Delta E_{{\rm{Theo}}} $, quadrupole deformations $ \beta_{20} $, $ \beta_{22} $ and octupole deformations $ \beta_{30} $, $ \beta_{31} $, $ \beta_{32} $, $ \beta_{33} $ of fission inner barrier, outer barrier, and isomeric states of 7 actinide nuclei obtained by 3DRDFT with $ V_{4} $ symmetry breaking.
核素 $ ^{232}{\rm{U}} $ $ ^{234}{\rm{U}} $ $ ^{236}{\rm{U}} $ $ ^{238}{\rm{U}} $ $ ^{236}{\rm{Pu}} $ $ ^{238}{\rm{Pu}} $ $ ^{240}{\rm{Pu}} $ 内垒 $ \Delta E_{{\rm{Exp}}}\ [{\rm{MeV]}} $ 4.90 4.80 5.00 6.30 - 5.60 6.05 $ \Delta E_{{\rm{Theo}}}\ [{\rm{MeV]}} $ 4.59 5.24 5.13 5.70 5.94 5.75 6.12 $ \beta_{20} $ 0.60 0.60 0.60 0.65 0.60 0.60 0.65 $ \beta_{22} $ 0.04 0.06 0.06 0.06 0.06 0.06 0.06 $ \beta_{30} $ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 $ \beta_{31} $ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 $ \beta_{32} $ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 $ \beta_{33} $ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 外垒 $ \Delta E_{{\rm{Exp}}}\ [{\rm{MeV]}} $ 5.40 5.50 5.67 5.50 - 5.10 5.15 $ \Delta E_{{\rm{Theo}}}\ [{\rm{MeV]}} $ 5.45 6.06 5.58 5.78 5.15 5.02 5.12 $ \beta_{20} $ 1.20 1.20 1.35 1.35 1.20 1.25 1.40 $ \beta_{22} $ 0.03 0.03 0.03 0.03 0.03 0.03 0.02 $ \beta_{30} $ 0.41 0.37 0.39 0.50 0.35 0.30 0.51 $ \beta_{31} $ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 $ \beta_{32} $ 0.02 0.01 0.00 0.00 0.02 0.01 0.01 $ \beta_{33} $ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 同核异能态 $ \Delta E_{{\rm{Exp}}}\ [{\rm{MeV]}} $ - - 2.3 2.6 - 2.4 2.25 $ \Delta E_{{\rm{Theo}}}\ [{\rm{MeV]}} $ 2.1 1.2 1.2 1.2 1.4 1.4 1.4 $ \beta_{20} $ 0.85 0.90 0.90 1.00 0.90 0.90 0.95 $ \beta_{22} $ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 $ \beta_{30} $ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 $ \beta_{31} $ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 $ \beta_{32} $ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 $ \beta_{33} $ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 
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[1] Schmidt K H, Jurado B 2018 Rep. Prog. Phys. 81 106301
Google Scholar
[2] Bender M, Bernard R, Bertsch G, Chiba S, Dobaczewski J, Dubray N, Giuliani S A, Hagino K, Lacroix D, Li Z, Magierski P, Maruhn J, Nazarewicz W, Pei J, Péru S, Pillet N, Randrup J, Regnier D, Reinhard P G, Robledo L M, Ryssens W, Sadhukhan J, Scamps G, Schunck N, Simenel C, Skalski J, Stetcu I, Stevenson P, Umar S, Verriere M, Vretenar D, Warda M, Åberg S 2020 J. Phys. G: Nucl. Part. Phys. 47 113002
Google Scholar
[3] Schunck N, Robledo L M 2016 Rep. Prog. Phys. 79 116301
Google Scholar
[4] Schunck N, Regnier D 2022 Prog. Part. Nucl. Phys. 125 103963
Google Scholar
[5] Hofmann S, Münzenberg G 2000 Rev. Mod. Phys. 72 733
Google Scholar
[6] Oganessian Y T, Abdullin F S, Bailey P D, Benker D E, Bennett M E, Dmitriev S N, Ezold J G, Hamilton J H, Henderson R A, Itkis M G, Lobanov Y V, Mezentsev A N, Moody K J, Nelson S L, Polyakov A N, Porter C E, Ramayya A V, Riley F D, Roberto J B, Ryabinin M A, Rykaczewski K P, Sagaidak R N, Shaughnessy D A, Shirokovsky I V, Stoyer M A, Subbotin V G, Sudowe R, Sukhov A M, Tsyganov Y S, Utyonkov V K, Voinov A A, Vostokin G K, Wilk P A 2010 Phys. Rev. Lett. 104 142502
Google Scholar
[7] Möller P, Sierk A J, Ichikawa T, Iwamoto A, Bengtsson R, Uhrenholt H, Åberg S 2009 Phys. Rev. C 79 064304
[8] Pei J C, Nazarewicz W, Sheikh J A, Kerman A K 2009 Phys. Rev. Lett. 102 192501
Google Scholar
[9] Korobkin O, Rosswog S, Arcones A, Winteler C 2012 Mon. Not. R. Astron. Soc. 426 1940
Google Scholar
[10] Just O, Bauswein A, Pulpillo R A, Goriely S, Janka H T 2015 Mon. Not. R. Astron. Soc. 448 541
Google Scholar
[11] Chen J W, Pei J C, Qiang Y, Chi J H 2023 Chin. Phys. Lett. 40 012401
Google Scholar
[12] Möller P, Madland D, Sierk A, Iwamoto A 2001 Nature 409 785790
[13] Pomorski K, Dudek J 2003 Phys. Rev. C 67 044316
Google Scholar
[14] Ivanyuk F A, Pomorski K 2009 Phys. Rev. C 79 054327
Google Scholar
[15] Kowal M, Jachimowicz P, Sobiczewski A 2010 Phys. Rev. C 82 014303
[16] Royer G, Jaffré M, Moreau D 2012 Phys. Rev. C 86 044326
Google Scholar
[17] Mamdouh A, Pearson J, Rayet M, Tondeur F 2001 Nucl. Phys. A 679 337
Google Scholar
[18] Bürvenich T, Bender M, Maruhn J A, Reinhard P G 2004 Phys. Rev. C 69 014307
Google Scholar
[19] Samyn M, Goriely S, Pearson J M 2005 Phys. Rev. C 72 044316
Google Scholar
[20] Minato F, Chiba S, Hagino K 2009 Nucl. Phys. A 831 150
Google Scholar
[21] Egido J L, Robledo L M 2000 Phys. Rev. Lett. 85 1198
Google Scholar
[22] Kortelainen M, McDonnell J, Nazarewicz W, Reinhard P G, Sarich J, Schunck N, Stoitsov M V, Wild S M 2012 Phys. Rev. C 85 024304
[23] McDonnell J, Schunck N, Nazarewicz W 2013 in Fission and Properties of Neutron-Rich Nuclei: Proceedings of the Fifth International Conference on Fission and Properties of Neutron-Rich Nuclei (ICFN5) (Singapore: World Scientific Publishing Company) pp597–604
[24] Staszczak A, Baran A, Nazarewicz W 2013 Phys. Rev. C 87 024320
Google Scholar
[25] Schunck N, Duke D, Carr H, Knoll A 2014 Phys. Rev. C 90 054305
[26] Blum V, Maruhn J A, Reinhard P G, Greiner W 1994 Phys. Lett. B 323 262
Google Scholar
[27] Zhang W, Zhang S S, Zhang S Q, Meng J 2003 Chin. Phys. Lett. 20 1694
Google Scholar
[28] Lü H F, Geng L S, Meng J 2006 Chin. Phys. Lett. 23 2940
Google Scholar
[29] Li Z P, Nikšić T, Vretenar D, Ring P, Meng J 2010 Phys. Rev. C 81 064321
Google Scholar
[30] Abusara H, Afanasjev A V, Ring P 2010 Phys. Rev. C 82 044303
[31] Lu B N, Zhao E G, Zhou S G 2012 Phys. Rev. C 85 011301
Google Scholar
[32] Lu B N, Zhao J, Zhao E G, Zhou S 2012 EPJ Web Conf. 38 05003
Google Scholar
[33] Abusara H, Afanasjev A V, Ring P 2012 Phys. Rev. C 85 024314
Google Scholar
[34] Prassa V, Nikšić T, Lalazissis G A, Vretenar D 2012 Phys. Rev. C 86 024317
Google Scholar
[35] Möller P, Sierk A J, Iwamoto A 2004 Phys. Rev. Lett. 92 072501
Google Scholar
[36] Brack M, Damgaard J, Jensen A S, Pauli H C, Strutinsky V M, Wong C Y 1972 Rev. Mod. Phys. 44 320
Google Scholar
[37] Pashkevich V 1969 Nucl. Phys. A 133 400
Google Scholar
[38] Möller P, Nilsson S G 1970 Phys. Lett. B 31 283
[39] Randrup J, Larsson S E, Möller P, Nilsson S G, Pomorski K, Sobiczewski A 1976 Phys. Rev. C 13 229
[40] Pashkevich V 1971 Nucl. Phys. A 169 275
Google Scholar
[41] Pauli H C, Ledergerber T, Brack M 1971 Phys. Lett. B 34 264
Google Scholar
[42] Bender M, Heenen P H, Reinhard P G 2003 Rev. Mod. Phys. 75 121
Google Scholar
[43] Meng J 2016 Relativistic Density Functional for Nuclear Structure (Singapore: World Scientific) p716
[44] Girod M, Grammaticos B 1983 Phys. Rev. C 27 2317
Google Scholar
[45] Rutz K, Maruhn J, Reinhard P G, Greiner W 1995 Nucl. Phys. A 590 680
Google Scholar
[46] Bonneau L, Quentin P, Samsœn D 2004 Eur. Phys. J. A 21 391
Google Scholar
[47] Ryssens W, Scamps G, Goriely S, Bender M 2022 Eur. Phys. J. A 50 246
[48] Ryssens W, Scamps G, Goriely S, Bender M 2023 Eur. Phys. J. A 59 96
Google Scholar
[49] Lu B N, Zhao J, Zhao E G, Zhou S G 2014 Phys. Rev. C 89 014323
Google Scholar
[50] 马中骐 2006 物理学中的群论(北京: 科学出版社) 第22页
Ma Z Q 2006 Group Theory in Physics (Peking: Science Press) p22
[51] Ren Z X, Zhang S Q, Meng J 2017 Phys. Rev. C 95 024313
Google Scholar
[52] Li B, Ren Z X, Zhao P W 2020 Phys. Rev. C 102 044307
Google Scholar
[53] Xu F F, Li B, Ren Z X, Zhao P W 2024 Phys. Rev. C 109 014311
[54] Ring P 1996 Prog. Part. Nucl. Phys. 37 193
Google Scholar
[55] Ren Z X, Zhao P W 2020 Phys. Rev. C 102 021301
Google Scholar
[56] Vretenar D, Afanasjev A, Lalazissis G, Ring P 2005 Phys. Rep. 409 101
Google Scholar
[57] Meng J, Peng J, Zhang S Q, Zhao P W 2013 Front. Phys. 8 55
Google Scholar
[58] Ren Z X, Zhang S Q, Zhao P W, N I, Maruhn J A, Meng J 2019 Sci. China Phys. Mech. Astron. 62 112062
Google Scholar
[59] Ren Z X, Zhao P W, Zhang S Q, Meng J 2020 Nucl. Phys. A 996 121696
Google Scholar
[60] Xu F F, Li B, Ring P, Zhao P W 2024 Phys. Lett. B 856 138893
Google Scholar
[61] Ren Z X, Zhao P W, Meng J 2022 Phys. Rev. C 105 L011301
[62] Li B, Zhao P W, Meng J 2024 Phys. Lett. B 856 138877
Google Scholar
[63] Xu F F, Wang Y K, Wang Y P, Ring P, Zhao P W 2024 Phys. Rev. Lett. 133 022501
Google Scholar
[64] Zhao P W, Li Z P, Yao J M, Meng J 2010 Phys. Rev. C 82 054319
Google Scholar
[65] Yang Y L, Wang Y K, Zhao P W, Li Z P 2021 Phys. Rev. C 104 054312
Google Scholar
[66] Yang Y L, Zhao P W, Li Z P 2023 Phys. Rev. C 107 024308
Google Scholar
[67] Ryssens W, Hellemans V, Bender M, Heenen P H 2015 Comput. Phys. Commun. 190 231
Google Scholar
[68] Bender M, Rutz K, Reinhard P, Maruhn J A 2000 Eur. Phys. J. A 8 59
Google Scholar
[69] Staszczak A, Stoitsov M, Baran A, Nazarewicz W 2010 Eur. Phys. J. A 46 85
Google Scholar
[70] Wang M, Huang W, Kondev F, Audi G, Naimi S 2021 Chin. Phys. C 45 030003
Google Scholar
[71] Kondev F, Wang M, Huang W, Naimi S, Audi G 2021 Chin. Phys. C 45 030001
Google Scholar
[72] Wang M, Audi G, Kondev F, Huang W J, Naimi S, Xu X 2017 Chin. Phys. C 41 030003
Google Scholar
[73] Agbemava S E, Afanasjev A V, Ray D, Ring P 2014 Phys. Rev. C 89 054320
Google Scholar
[74] Ring P, Schuck P 1980 The Nuclear Many-Body Problem (Heidelberg: Springer Berlin) pp244–279
[75] Capote R, Herman M, Obložinský P, Young P, Goriely S, Belgya T, Ignatyuk A, Koning A, Hilaire S, Plujko V, Avrigeanu M, Bersillon O, Chadwick M, Fukahori T, Ge Z, Han Y, Kailas S, Kopecky J, Maslov V, Reffo G, Sin M, Soukhovitskii E, Talou P 2009 Nucl. Data Sheets 110 3107
Google Scholar
[76] Singh B, Zywina R, Firestone R B 2002 Nucl. Data Sheets 97 241
Google Scholar
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