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.

Figures (8)

• Figure 1: Comparison of the predicted SF half-lives for even-even Uranium and Flerovium isotopes. The squares denote the experimental data taken from NUBASE2020 NUBASE2020. The solid curve and the dot-dashed curve denote the results of XRG formula proposed in Ren08 and those of MAA formula in Anto25, respectively.
• Figure 2: (Color online) (a) Measured maximum of $\log_{10} T_{\rm SF}$ in each isotopic chain with mass numbers from $A=232$ to $A=286$. (b) The corresponding values of the effective tunneling barrier $U$. The red curve denotes the relative barrier height $U_0=V_{\rm top}-Q_{\rm sf}+\Delta$.
• Figure 3: (Color online) Spontaneous fission half-lives of even-even actinides. The black curves denote the calculated results with Eq.(7) and the red open symbols denote the experimental data taken from NUBASE2020 NUBASE2020.
• Figure 4: (Color online) Deviations of model predictions from the experimental half-lives. The circles and the squares denote the results with the proposed ETB approach and those of the MAA formula Anto25, respectively.
• Figure 5: (Color online) Deviations between the measured half-lives and the predictions with Eq.(7) but neglecting the $Q_\alpha$ term. (a) for even-even nuclei and (b) for odd-A nuclei.