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

$\alpha$ 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 in $\alpha$ 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.

Figure 1

Measured half-lives of ground states of Cf, Fm, No, and Rf isotopes. Main decay modes are indicated by different symbols given in the legend.

Figure 2

The $\alpha$ decay energy between ground states of the parent and daughter nuclei of Rn, Th, Pu, Cf, No, Sg, and Ds isotopes.

Figure 3

Logarithmic of deviations between the calculated half-lives and experimental data as a function of neutron numbers, showing the comparison of (a) in a unified way, (b) separately treating the $\alpha$ preformation probability of even $Z$, odd $N$ and odd $Z$, even $N$ nuclei in region III.

Figure 4

The comparison of the estimated $\alpha$ preformation probability between the even-odd and odd-even nuclei in region III as a function of the neutron numbers of the parent nuclei.

Figure 5

Logarithmic of deviations between the calculated half-lives and experimental data as a function of neutron numbers of the parent nuclei.