Error _selectel_forbidden_access
Везде

RAS PhysicsЯдерная физика Physics of Atomic Nuclei

  • ISSN (Print) 0044-0027
  • ISSN (Online) 3034-6282

Semi-empirical formula for spontaneous fission half-life calculation

You can
PII
S3034628225050011-1
DOI
10.7868/S3034628225050011
Publication type
Article
Status
Published
Authors
N. S. Moiseev
  • Occupation: Bogoliubov Laboratory of Theoretical Physics
  • Affiliation:
    Joint Institute for Nuclear Research
    Tomsk Polytechnic University
N. V. Antonenko
  • Occupation: Bogoliubov Laboratory of Theoretical Physics
  • Affiliation:
    Joint Institute for Nuclear Research
    Tomsk Polytechnic University
G. G. Adamian
  • Occupation: Bogoliubov Laboratory of Theoretical Physics
  • Affiliation: Joint Institute for Nuclear Research
Volume/ Edition
Volume 88 / Issue number 5
Pages
381-399
Abstract
This work presents a new phenomenological approach for predicting the spontaneous fission half-lives of actinides and superheavy nuclei. A linear dependence between the decimal logarithm of the spontaneous fission half-life log T and the energy release Q of alpha decay is found for nuclei with fixed neutron excess N – Z and atomic numbers in the range 90 ≤ Z ≤ 102. Based on this correlation, a semi-empirical formula is proposed for the spontaneous fission half-life of even–even nuclei as a function of Q and N – Z. The proposed formula is further extended to predict half-lives for odd–A, odd–odd nuclei, and nuclei with Z ≥ 103. The formula demonstrates good agreement with experimental data, reproducing the half-lives of 111 known nuclei with a mean deviation of 1.00 order of magnitude. Predictions of the new formula are compared with results obtained using other empirical formulas and microscopic–macroscopic and self-consistent microscopic models. An analysis of the influence of different mass tables on the accuracy of the predictions is performed. The possible fundamental relationship between spontaneous fission and alpha-decay processes is discussed.
Keywords
сверхтяжелые ядра деление ядер период полураспада феноменология
Date of publication
01.02.2026
Year of publication
2026
Number of purchasers
0
Views
11

References

  1. 1. Y. T. Oganessian, Eur. Phys. J. A , 227 (2024).
  2. 2. Y. T. Oganessian, V. K. Utyonkov, N. D. Kovrizhnykh, F. S. Abdullin, S. N. Dmitriev, D. Ibadullayev, M. G. Itkis, D. A. Kuznetsov, O. V. Petrushkin, A. V. Podshibiakin, , Phys. Rev. C , L031301 (2022).
  3. 3. Y. T. Oganessian, V. K. Utyonkov, D. Ibadullayev, F. S. Abdullin, S. N. Dmitriev, M. G. Itkis, A. V. Karpov, N. D. Kovrizhnykh, D. A. Kuznetsov, O. V. Petrushkin, , Phys. Rev. C , 024612 (2022).
  4. 4. Y. T. Oganessian, V. K. Utyonkov, N. D. Kovrizhnykh, F. S. Abdullin, S. N. Dmitriev, A. A. Dzhioev, D. Ibadullayev, M. G. Itkis, A. V. Karpov, D. A. Kuznetsov, , Phys. Rev. C , 064306 (2022).
  5. 5. Y. T. Oganessian, V. K. Utyonkov, M. V. Shumeiko, F. S. Abdullin, S. N. Dmitriev, D. Ibadullayev, M. G. Itkis, N. D. Kovrizhnykh, D. A. Kuznetsov, O. V. Petrushkin, , Phys. Rev. C , 024611 (2023).
  6. 6. Y. T. Oganessian, V. K. Utyonkov, M. V. Shumeiko, F. S. Abdullin, G. Adamian, S. N. Dmitriev, D. Ibadullayev, M. G. Itkis, N. D. Kovrizhnykh, D. A. Kuznetsov, , Phys. Rev. C , 054307 (2024).
  7. 7. D. Ackermann, S. Antalic, and F. P. Heßberger, Eur. Phys. J. Spec. Top. , 1017 (2024).
  8. 8. E. M. Kozulin, G. N. Knyazheva, A. V. Karpov, V. V. Saiko, A. A. Bogachev, I. M. Itkis, K. V. Novikov, I. V. Vorobiev, I. V. Pchelintsev, E. O. Savelieva, , Phys. Rev. C , 034616 (2024).
  9. 9. K. Kessaci, B. J. P. Gall, O. Dorvaux, M. Forge, A. Lopez-Martens, R. Chakma, K. Hauschild, M. L. Chelnokov, V. I. Chepigin, A. V. Isaev, , Phys. Rev. C , 054310 (2024).
  10. 10. G. Münzenberg, M. Gupta, H. M. Devaraja, Y. K. Gambhir, S. Heinz, and S. Hofmann, Eur. Phys. J. A , 21 (2023).
  11. 11. A. Såmark-Roth, D. M. Cox, D. Rudolph, L. G. Sarmiento, B. G. Carlsson, J. L. Egido, P. Golubev, J. Heery, A. Yakushev, S. Åberg, , Phys. Rev. Lett. , 032503 (2021).
  12. 12. G. G. Adamian, N. V. Antonenko, A. Diaz-Torres, and S. Heinz, Eur. Phys. J. A , 47 (2020).
  13. 13. Y. Oganessian, J. Phys. G: Nucl. Part. Phys. , R165 (2007).
  14. 14. Y. T. Oganessian and V. K. Utyonkov, Nucl. Phys. A , 62 (2015).
  15. 15. Y. T. Oganessian and V. K. Utyonkov, Rep. Prog. Phys. , 036301 (2015).
  16. 16. S. Hofmann, S. Heinz, R. Mann, J. Maurer, G. Münzenberg, S. Antalic, W. Barth, H. G. Burkhard, L. Dahl, K. Eberhardt, , Eur. Phys. J. A , 180 (2016).
  17. 17. K. Morita, Nucl. Phys. A , 30 (2015).
  18. 18. S. Hofmann and G. Münzenberg, Rev. Mod. Phys. , 733 (2000).
  19. 19. K. E. Gregorich, J. M. Gates, C. E. Düllmann, R. Sudowe, S. L. Nelson, M. A. Garcia, I. Dragojević, C. M. Folden , S. H. Neumann, D. C. Hoffman, , Phys. Rev. C , 044611 (2006).
  20. 20. J. Dvorak, W. Brüchle, M. Chelnokov, R. Dressler, C. E. Düllmann, K. Eberhardt, V. Gorshkov, E. Jäger, R. Krücken, A. Kuznetsov, , Phys. Rev. Lett. , 242501 (2006).
  21. 21. D. Peterson, B. B. Back, R. V. F. Janssens, T. L. Khoo, C. J. Lister, D. Seweryniak, I. Ahmad, M. P. Carpenter, C. N. Davids, A. A. Hecht, , Phys. Rev. C , 014316 (2006).
  22. 22. S. Hofmann, S. Heinz, R. Mann, J. Maurer, G. Münzenberg, S. Antalic, W. Barth, L. Dahl, K. Eberhardt, R. Grzywacz, , Eur. Phys. J. A , 116 (2016).
  23. 23. F. P. Heßberger, Eur. Phys. J. A , 75 (2017).
  24. 24. J. Khuyagbaatar, H. Brand, R. A. Cantemir, C. E. Düllmann, F. P. Heßberger, E. Jäger, B. Kindler, J. Krier, N. Kurz, B. Lommel, , Phys. Rev. C , L031303 (2021).
  25. 25. K. Morita, K. Morimoto, D. Kaji, T. Akiyama, S.-I. Goto, H. Haba, E. Ideguchi, K. Katori, H. Koura, and H. Kudo, J. Phys. Soc. Jpn , 043201 (2007).
  26. 26. И. В. Панов, И. Ю. Корнеев, Г. Мартинец-Пинедо, Ф. К. Тилеманн, Письма в Астрон. журн. , 173 (2013).
  27. 27. Y. T. Oganessian, V. K. Utyonkov, Y. V. Lobanov, F. S. Abdullin, A. N. Polyakov, I. V. Shirokovsky, Y. S. Tsyganov, G. G. Gulbekian, S. L. Bogomolov, B. N. Gikal, , Phys. Rev. C , 064609 (2004).
  28. 28. Y. T. Oganessian, V. K. Utyonkov, S. N. Dmitriev, Y. V. Lobanov, M. G. Itkis, A. N. Polyakov, Y. S. Tsyganov, A. N. Mezentsev, A. V. Yeremin, A. A. Voinov, , Phys. Rev. C , 034611 (2005).
  29. 29. Y. T. Oganessian, V. K. Utyonkov, Y. V. Lobanov, F. S. Abdullin, A. N. Polyakov, R. N. Sagaidak, I. V. Shirokovsky, Y. S. Tsyganov, A. A. Voinov, G. G. Gulbekian, , Phys. Rev. C , 044602 (2006).
  30. 30. R. Smolańczuk, J. Skalski, and A. Sobiczewski, Phys. Rev. C , 1871 (1995).
  31. 31. R. Smolańczuk, Phys. Rev. C , 812 (1997).
  32. 32. M. Warda and J. L. Egido, Phys. Rev. C , 014322 (2012).
  33. 33. A. Staszczak, A. Baran, and W. Nazarewicz, Phys. Rev. C , 024320 (2013).
  34. 34. T. Ichikawa, A. Iwamoto, and P. Möller, Phys. Rev. C , 014305 (2009).
  35. 35. P. Jachimowicz, M. Kowal, and J. Skalski, Phys. Rev. C , 014311 (2020).
  36. 36. S. Giuliani, L. Robledo, and R. Rodriguez-Guzman, Phys. Rev. C , 054311 (2014).
  37. 37. C. Xu and Z. Ren, Phys. Rev. C , 014309 (2005).
  38. 38. W. J. Swiatecki, Phys. Rev. , 937 (1955).
  39. 39. D. W. Dorn, Phys. Rev. , 1740 (1961).
  40. 40. V. E. Viola and G. T. Seaborg, J. Inorg. Nucl. Chem. , 741 (1966).
  41. 41. Z. Ren and C. Xu, Nucl. Phys. A , 64 (2005).
  42. 42. C. Xu, Z. Ren, and Y. Guo, Phys. Rev. C , 044329 (2008).
  43. 43. K. P. Santhosh, R. K. Biju, and S. Sahadevan, Nucl. Phys. A , 220 (2010).
  44. 44. A. V. Karpov, V. I. Zagrebaev, Y. Martinez Palenzuela, L. F. Felipe Ruiz, and W. Greiner, Int. J. Mod. Phys. E , 1250013 (2012).
  45. 45. A. Zdeb, M. Warda, and K. Pomorski, Phys. Scr. , 054015 (2014).
  46. 46. X. J. Bao, S. Q. Guo, H. F. Zhang, Y. Z. Xing, J. M. Dong, and J. Q. Li, J. Phys. G: Nucl. Par. Phys. , 085101 (2015).
  47. 47. K. P. Santhosh and C. Nithya, Phys. Rev. C , 054621 (2016).
  48. 48. Z. Yuan, D. Bai, Z. Wang, and Z. Ren, Eur. Phys. J. A , 68 (2024).
  49. 49. A. V. M. Babu, N. Dhananjaya, H. C. Manjunatha, N. Sowmya, and A. M. Nagaraja, Mod. Phys. Lett. A , 2450018 (2024).
  50. 50. K. Pomorski and J. Dudek, Phys. Rev. C , 044316 (2003).
  51. 51. P. Möller, J. R. Nix, W. D. Myers, and W. J. Swiatecki, At. Data Nucl. Data Tables , 185 (1995).
  52. 52. F. Kondev, M. Wang, W. Huang, S. Naimi, and G. Audi, Chin. Phys. C , 030001 (2021).
  53. 53. G. Adamian, N. Antonenko, and W. Scheid, Clustering Effects Within the Dinuclear Model (Springer Berlin Heidelberg, Berlin, Heidelberg, 2012), Vol. 2, p. 165.
  54. 54. I. Rogov, G. Adamyan, and N. Antonenko, EPJ Web Conf. 194, 06005 (2018).
  55. 55. I. S. Rogov, G. G. Adamian, and N. V. Antonenko, Phys. Rev. C 100, 024606 (2019).
  56. 56. I. S. Rogov, G. G. Adamian, and N. V. Antonenko, Phys. Rev. C 104, 034618 (2021).
  57. 57. I. S. Rogov, G. G. Adamian, and N. V. Antonenko, Phys. Rev. C 105, 034619 (2022).
  58. 58. I. S. Rogov, G. G. Adamian, and N. V. Antonenko, Phys. Rev. C 110, 014606 (2024).
  59. 59. H. Fink, J. Maruhn, W. Scheid, and W. Greiner, Z. Phys. 268, 321 (1974).
  60. 60. D. Poenaru and R. Gherghescu, Phys. Rev. C 97, 044621 (2018).
  61. 61. D. Poenaru, I.-H. Plonski, and W. Greiner, Phys. Rev. C 74, 014312 (2006).
  62. 62. D. Poenaru, M. Ivascu, A. Sandulescu, and W. Greiner, Phys. Rev. C 32, 572 (1985).
  63. 63. S. Malik and R. Gupta, Phys. Rev. C 39, 1992 (1989).
  64. 64. W. Seif, Phys. Rev. C 74, 034302 (2006).
  65. 65. M. Wang, W. J. Huang, F. G. Kondev, G. Audi, and S. Naimi, Chin. Phys. C 45, 030003 (2021).
  66. 66. J. Dong, W. Zuo, and W. Scheid, Phys. Rev. Lett. 107, 012501 (2011).
  67. 67. Y. T. Oganesyan, Y. P. Tret’yakov, A. S. Il’inov, A. G. Demin, A. A. Pleve, S. P. Tret’yakova, V. M. Plotko, M. P. Ivanov, N. A. Danilov, Y. S. Korotkin, et al., Tech. Rep., Joint Institute for Nuclear Research (1974).
  68. 68. Y. T. Oganessian, A. S. Iljinov, A. G. Demin, and S. P. Tretyakova, Nucl. Phys. A 239, 353 (1975).
  69. 69. A. Türler, H. W. Gäggeler, D. T. Jost, P. Armbruster, W. Brüchle, H. Folger, F. P. Heßberger, S. Hofmann, G. Münzenberg, V. Ninov, et al., Z. Phys. A 331, 363 (1988).
  70. 70. F. P. Heßberger, S. Hofmann, V. Ninov, P. Armbruster, H. Folger, G. Münzenberg, H. J. Schött, A. G. Popeko, A. V. Yeremin, A. N. Andreyev, et al., Z. Phys. A 359, 415 (1997).
  71. 71. D. C. Hoffman and M. R. Lane, Radiochimica Acta 70/71, 135 (1995).
  72. 72. A. I. Svirikhin, A. V. Yeremin, N. I. Zamyatin, I. N. Izosimov, A. V. Isaev, A. A. Kuznetsova, O. N. Malyshev, R. S. Mukhin, A. G. Popeko, Y. A. Popov, et al., Phys. Part. Nucl. Lett. 18, 445 (2021).
  73. 73. Y. A. Lazarev, Y. V. Lobanov, Y. T. Oganessian, V. K. Utyonkov, F. S. Abdullin, A. N. Polyakov, J. Rigol, I. V. Shirokovsky, Y. S. Tsyganov, S. Iliev, et al., Phys. Rev. C 62, 064307 (2000).
  74. 74. M. Murakami, S. Goto, H. Murayama, T. Kojima, H. Kudo, D. Kaji, K. Morimoto, H. Haba, Y. Kudou, T. Sumita, et al., Phys. Rev. C 88, 024618 (2013).
  75. 75. S. Antalic, F. Heßberger, S. Hofmann, D. Ackermann, S. Heinz, B. Kindler, I. Kojouharov, P. Kuusiniemi, M. Leino, B. Lommel, et al., Eur. Phys. J. A 38, 219 (2008).
  76. 76. S. Antalic, F. Heßberger, D. Ackermann, S. Heinz, S. Hofmann, B. Kindler, J. Khuyagbaatar, B. Lommel, and R. Mann, Eur. Phys. J. A 51, 1 (2015).
  77. 77. S. L. Nelson, K. E. Gregorich, I. Dragojevi´c, M. A. Garcia, J. M. Gates, R. Sudowe, and H. Nitsche, Phys. Rev. Lett. 100, 022501 (2008).
  78. 78. F. P. Hessberger, J. Phys. G: Nucl.Part. Phys. 25, 877 (1999).
  79. 79. Y. T. Oganessian, V. K. Utyonkov, F. S. Abdullin, S. N. Dmitriev, R. Graeger, R. A. Henderson, M. G. Itkis, Y. V. Lobanov, A. N. Mezentsev, K. J. Moody, et al., Phys. Rev. C 87, 034605 (2013).
  80. 80. A. J. Hughes and D. E. Grawoig, Statistics, a foundation for analysis (Addison-Wesley Pub. Co., 1971).
  81. 81. J. Khuyagbaatar, F. P. Heßberger, S. Hofmann, D. Ackermann, V. S. Comas, S. Heinz, J. A. Heredia, B. Kindler, I. Kojouharov, B. Lommel, et al., Eur. Phys. J. A 46, 59 (2010).
  82. 82. E. K. Hulet, R. W. Lougheed, J. F. Wild, R. J. Dougan, K. J. Moody, R. L. Hahn, C. M. Henderson, R. J. Dupzyk, and G. R. Bethune, Phys. Rev. C 34, 1394 (1986).
  83. 83. J. M. Gates, C. E. Düllmann, M. Schädel, A. Yakushev, A. Türler, K. Eberhardt, J. V. Kratz, D. Ackermann, L.-L. Andersson, M. Block, et al., Phys. Rev. C 83, 054618 (2011).
  84. 84. Y. T. Oganessian, V. K. Utyonkov, Y. V. Lobanov, F. S. Abdullin, A. N. Polyakov, I. V. Shirokovsky, Y. S. Tsyganov, G. G. Gulbekian, S. L. Bogomolov, B. N. Gikal, et al., Phys. Rev. Lett. 83, 3154 (1999).
  85. 85. P. Möller, J. R. Nix, and W. J. Swiatecki, Nucl. Phys. A 492, 349 (1989).
  86. 86. P. Jachimowicz, M. Kowal, and J. Skalski, Phys. Rev. C 95, 014303 (2017).
  87. 87. Z. Wang and Z. Ren, Phys. Rev. C 106, 024311 (2022).
  88. 88. Z. Yuan, D. Bai, Z. Wang, Z. Ren, and D. Ni, Science China: Physics, Mechanics & Astronomy 66, 222012 (2023).
  89. 89. J. Liu, Z. Wang, H. Zhang, and Z. Ren, Chin. Phys. C 48, 014105 (2024).
  90. 90. N. Wang, M. Liu, X. Wu, and J. Meng, Phys. Lett. B 734, 215 (2014).
  91. 91. N. Wang, Nuclear mass table with WS4 model (2014), https://www.researchgate.net/publication/307865750_Nuclear_mass_table_with_WS4_model
  92. 92. P. Möller, A. J. Sierk, T. Ichikawa, and H. Sagawa, At. Data Nucl. Data Tables 109, 1 (2016).
  93. 93. P. Jachimowicz, M. Kowal, and J. Skalski, At. Data Nucl. Data Tables 138, 101393 (2021).
  94. 94. K. Zhang, M.-K. Cheoun, Y.-B. Choi, P. S. Chong, J. Dong, L. Geng, E. Ha, X. He, C. Heo, M. C. Ho, et al., Phys. Rev. C 102, 024314 (2020).
  95. 95. K. Zhang, M.-K. Cheoun, Y.-B. Choi, P. S. Chong, J. Dong, Z. Dong, X. Du, L. Geng, E. Ha, X.-T. He, et al., At. Data Nucl. Data Tables 144, 101488 (2022).
  96. 96. P. Guo, X. Cao, K. Chen, Z. Chen, M.-K. Cheoun, Y.-B. Choi, P. C. Lam, W. Deng, J. Dong, P. Du, et al., At. Data Nucl. Data Tables 158, 101661 (2024).
  97. 97. The BSkG3 model, http://www.astro.ulb.ac.be/pmwiki/Brusslib/BSkG3
  98. 98. G. Scamps, S. Goriely, E. Olsen, M. Bender, and W. Ryssens, Eur. Phys. J. A 57, 1 (2021).
  99. 99. W. Ryssens, G. Scamps, S. Goriely, and M. Bender, Eur. Phys. J. A 58, 246 (2022).
  100. 100. W. Ryssens, G. Scamps, S. Goriely, and M. Bender, Eur. Phys. J. A 59, 96 (2023).
  101. 101. G. Grams, W. Ryssens, G. Scamps, S. Goriely, and N. Chamel, Eur. Phys. J. A 59, 270 (2023).
  102. 102. J. Duflo and A. Zuker, Phys. Rev. C 52, R23 (1995).
  103. 103. J. Mendoza-Temis, J. G. Hirsch, and A. P. Zuker, Nucl. Phys. A 843, 14 (2010).
  104. 104. S. Liran, A. Marinov, and N. Zeldes, Hyperfine Interactions 132, 421 (2001).
  105. 105. S. Liran, A. Marinov, and N. Zeldes, nucl-th/0102055.
QR
Translate

Indexing

Scopus

Scopus

Scopus

Crossref

Scopus

Higher Attestation Commission

At the Ministry of Education and Science of the Russian Federation

Scopus

Scientific Electronic Library