Systematic study of favored \alpha-decay half-lives of closed shell odd-A and doubly-odd nuclei related to ground and isomeric states

TL;DR

This paper systematically studies alpha-decay half-lives and preformation probabilities of odd-A and doubly-odd nuclei near magic numbers, revealing linear relationships with valence nucleons and providing formulas that match experimental data.

Contribution

It introduces new analytic formulas for alpha preformation probabilities based on valence nucleons and isospin, improving half-life predictions for specific nuclei.

Findings

Alpha preformation probability is linearly related to valence nucleons and isospin.

Derived formulas accurately reproduce experimental alpha-decay half-lives.

The approach enhances understanding of alpha decay near closed shells.

Abstract

In this work, we systematically investigate the favored $\alpha$-decay half-lives and $\alpha$ 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 $\alpha$ preformation probability is linear 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 $\alpha$ 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 $\alpha$ preformation probabilities and the values of corresponding parameters. Using those formulas and the parameters, we calculate the $\alpha$-decay half-lives for those nuclei. The calculated results can well reproduce the experimental data.