Systematic study of $α$ decay for odd-$A$ nuclei within a two-potential approach
$α$ 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 $α$ decay. In this work, we systematically studied the $α$ decay half-lives of odd-$A$ nuclei, including both favored and unfavored $α$ decay within the two-potential approach based on the isospin dependent nuclear potential. The $α$ 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 $α$ decay half-lives data. The results indicate that in general the $α$ 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 $α$ decay. The calculated half-lives can well reproduce the experimental data.