Spontaneous fission half-lives for heavy and super-heavy nuclei from phenomenological models

Abstract

A phenomenological model is proposed for a systematic description of the spontaneous fission (SF) half-lives $T_{\rm SF}$ of heavy and super-heavy nuclei. Based on the effective tunneling barrier (ETB), the proposed approach reproduces the SF half-lives of 79 known nuclei with an average deviation of 0.8, which is $17\%$ smaller than that of the linear correlation approach recently proposed in [N. S. Moiseev, N. V. Antonenko and G. G. Adamian, Phys. Rev. C 112, 034607 (2025)]. For superheavy nuclei with $45\leqslant N-Z \leqslant 61$, the predicted SF half-lives from these two different phenomenological models are in good agreement with each other. The ETB calculations implies that the $β$-decay energy affects the SF half-lives of nuclei far from the $β$-stability line. For superheavy nuclei around the magic number $N=184$, the predicted $T_{\rm SF}$ of $^{304}$120 is much shorter than that of $^{298}$Fl. With predicted values of about $10 \sim 160$ ms for $T_{\rm SF}$, the unmeasured SHN $^{293}119 $ could survive for long enough to reach the focal-plane detector in detection systems like the gas-filled recoil separator SHANS in Lanzhou.