In the present work, the unfavored $\alpha$-decay half-lives and $\alpha$ 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 $N_p{N}_n$ or $N_p{N}_{n}I$, 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 $\alpha$ 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 $\alpha$ 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.

• Received 5 June 2017

DOI:https://doi.org/10.1103/PhysRevC.96.024318