Systematic study of the $α$ decay preformation factor of nuclei around the $\boldsymbol{Z=82}$, $\boldsymbol{N=126}$ shell closures within a generalized liquid drop model

Abstract

In this work, we systematically study the α decay preformation factors Pα and α decay half-lives of 152 nuclei around Z = 82, N = 126 closed shells based on a generalized liquid drop model while Pα is extracted from the ratio of the calculated α decay half-life to the experimental one. The results show that there is an obvious linear relationship between Pα and the product of valance protons (holes) Np and valance neutrons (holes) Nn. At the same time, we extract the α decay preformation factors values of even-even nuclei around Z = 82, N = 126 closed shells from the work of Sun et al. [J. Phys. G: Nucl. Part. Phys. 45, 075106 (2018)], in which the α decay preformation factors can be calculated by two different microscopic formulas. We find that the α decay preformation factors are also related to NpNn. Combining with our previous works [Sun et al.,