Analytic formula for estimating the α -particle preformation factor

Abstract

In the present work, we build a bridge between the $\ensuremath{\alpha}$ decay energy and the $\ensuremath{\alpha}$-particle preformation factor, and put forward an analytic formula for estimating the $\ensuremath{\alpha}$-particle preformation factor. With the help of this formula, experimental $\ensuremath{\alpha}$ decay half-lives of 535 nuclei varying from $6.90\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ to $6.34\ifmmode\times\else\texttimes\fi{}{10}^{26}$ s are reproduced within a factor of 1.81. Noticeably, for superheavy nuclei, calculated $\ensuremath{\alpha}$ decay half-lives can well reproduce experimental data and reduce the deviations significantly. This formula can be applied to estimate the $\ensuremath{\alpha}$-particle preformation factors and predict the $\ensuremath{\alpha}$ decay half-lives for unsynthesized superheavy nuclei, which would be useful for future experiments in synthesizing new superheavy elements and isotopes. This formula can shed light on microscopic nuclear structure information such as shell and odd-even staggering effects, and provide a positive signal for the existence of an island of stability for superheavy nuclei.