Improved formulas of spontaneous fission half-lives for heavy and superheavy nuclei

Abstract

Spontaneous fission is important for the research of heavy and superheavy nuclei. However, the accurate calculation of spontaneous fission half-lives remains an open problem in nuclear physics. In this work, we propose an improved formula for even-even nuclei based on the previous law of spontaneous fission half-lives [C. Xu et al., Phys. Rev. C 71, 014309 (2005)]. The average deviation is 0.98 for 42 even-even nuclei, which is reduced by 39.27% in orders of magnitude compared to that calculated using the previous formula. Then, we further extend the improved formula to calculate the half-lives for odd-A and odd-odd nuclei by incorporating either a blocking factor or generalized seniority to include the blocking effect on the spontaneous fission half-lives [Z. Ren et al., Nucl. Phys. A 759, 64 (2005)]. The experimental half-lives can be reasonably reproduced using the two improved formulas, with average deviations of 1.50 and 1.37 for 79 nuclei, respectively. These results demonstrate that the improved formulas are reliable for the calculations of spontaneous fission half-lives. Finally, we predict the spontaneous fission half-lives for some nuclei on the $\alpha$-decay chains of $^{293, 294}$119 and $^{294, 295}$120. The calculated results can be helpful in future research on spontaneous fission and the synthesis experiments of new elements.