# Systematic study of $\alpha$ decay for odd-$A$ nuclei within a two-potential approach

## TL;DR

This study systematically analyzes alpha decay half-lives of odd-A nuclei using a two-potential approach, incorporating shell effects and proton-neutron correlations to improve predictions of experimental data.

## Contribution

It introduces an analytic formula for alpha preformation probabilities considering shell structure and correlations, enhancing decay half-life calculations for odd-A nuclei.

## Key findings

- Preformation probabilities are slightly smaller for even-Z, odd-N nuclei.
- Odd-even staggering influences spontaneous fission more than alpha decay.
- Calculated half-lives match experimental data well.

## Abstract

$\alpha$ decay is usually associated with both ground and low-lying isomeric states of heavy and superheavy nuclei, and the unpaired nucleon plays a key role on $\alpha$ decay. In this work, we systematically studied the $\alpha$ decay half-lives of odd-$A$ nuclei, including both favored and unfavored $\alpha$ decay within the two-potential approach based on the isospin dependent nuclear potential. The $\alpha$ preformation probabilities are estimated by using an analytic formula taking into account the shell structure and proton-neutron correlation, and the parameters are obtained through the $\alpha$ decay half-lives data. The results indicate that in general the $\alpha$ preformation probabilities of even-$Z$, odd-$N$ nuclei are slightly smaller than the odd-$Z$, even-$N$ ones. We found that the odd-even staggering effect may play a more important role on spontaneous fission than $\alpha$ decay. The calculated half-lives can well reproduce the experimental data.