Systematic study of unfavored α-decay half-lives of closed-shell nuclei related to ground and isomeric states

In the present work, the unfavored alpha-decay half-lives and a preformation probabilities of closed-shell nuclei related to ground and isomeric states around Z = 82, N = 82 and 126 shell closures are investigated by adopting the two-potential approach from the perspective of valence nucleon (hole) and isospin asymmetry of the parent nucleus. The results indicate that alpha preformation probability has linear dependence on NpNn or NpNnI, the same as the case of favored alpha-decay in our previous work [X.-D. Sun et al., Phys. Rev. C 94, 024338 (2016)]. N-p, N-n, and I represent the number of valence protons (holes), the number of valence neutrons (holes), and the isospin of the parent nucleus, respectively. Fitting the a preformation probability data extracted from the differences between experimental data and calculated half-lives without a shell correction, we give two linear formulas of the a preformation probabilities and the values of corresponding parameters. Based on the formulas and corresponding parameters, we calculate the alpha-decay half-lives for those nuclei. The calculated results can well reproduce the experimental data.