Systematic study of favoredα-decay half-lives of closed shell odd-Aand doubly-odd nuclei related to ground and isomeric states

Abstract

In this work, we systematically investigate the favored $\ensuremath{\alpha}$-decay half-lives and $\ensuremath{\alpha}$ preformation probabilities of both odd-$A$ and doubly-odd nuclei related to ground and isomeric states around the doubly magic cores at $Z=82, N=82$ and at $Z=82, N=126$, respectively, within a two-potential approach from the view of the valence nucleon (or hole). The results show that the $\ensuremath{\alpha}$ preformation probability is linearly related to ${N}_{\text{p}}{N}_{\text{n}}$ or ${N}_{\text{p}}{N}_{\text{n}}I$, where ${N}_{\text{p}}, {N}_{\text{n}}$, and $I$ are the number of valence protons (or holes), the number of valence neutrons (or holes), and the isospin of the parent nucleus, respectively. Fitting the $\ensuremath{\alpha}$ preformation probabilities data extracted from the differences between experimental data and calculated half-lives without a shell correction, we give two analytic formulas of the $\ensuremath{\alpha}$ preformation probabilities and the values of corresponding parameters. Using those formulas and the parameters, we calculate the $\ensuremath{\alpha}$-decay half-lives for those nuclei. The calculated results can well reproduce the experimental data.