Effects of finite-range exchange terms and deformation on the α -decay half-lives using the B3Y N N interaction

Abstract

An extensive study on the barrier properties and $\ensuremath{\alpha}$-decay half-lives of nuclei within the mass range $89\ensuremath{\le}Z\ensuremath{\le}102$ is conducted using the effective Botswana-3-Yukawa (B3Y) $NN$ interaction, incorporating finite- and zero-range exchange forces. A key novelty of this work is the systematic analysis of nuclear deformation and exchange effects on half-lives along the isotopic chains. Particularly, for the finite- and zero-range exchange terms, this study investigates the appropriate strength of the Weizs\"acker term, ${C}_{s}$, which represents the surface contribution to the kinetic energy density. The penetration probability of the ground-state to ground-state $\ensuremath{\alpha}$ transitions is determined using the semiclassical Wentzel-Kramers-Brillouin (WKB) approximation by considering the Bohr-Sommerfeld quantization condition. The cluster formation model (CFM) is adopted to calculate the preformation probability ${S}_{\ensuremath{\alpha}}$. The driving potential reveals a cold valley at the canonical magic number ${N}_{D}=126$, affirming its shell closure property, while deformed subshell closures at $N=142$ and $N=152$ are also identified. These results align with predictions from Nilsson single-particle energies. A key finding of this study is that the inclusion of nuclear deformation significantly improves the accuracy of the calculated $\ensuremath{\alpha}$-decay half-lives. The analysis also shows that the term ${C}_{s}$ directly influences the nuclear surface energy, which in turn affects the potential barrier relevant to $\ensuremath{\alpha}$ decay. Specifically, a larger value of ${C}_{s}=\frac{1}{4}$ increases the potential barrier, leading to longer half-lives, while a smaller value of ${C}_{s}=\frac{1}{36}$ reduces the barrier, resulting in shorter half-lives. Importantly, for nuclei with $Z\ensuremath{\ge}96$, calculations involving finite-range exchange terms at ${C}_{s}=\frac{1}{36}$ yield the smallest root mean square error (RMSE), suggesting a better agreement with experimental data, and indicating its prospect for the study of superheavy nuclei.