$\alpha$-decay half-lives and $\alpha$-cluster preformation factors of nuclei around $N=Z$ line

Abstract

In this work, a microscopic effective nucleon-nucleon interaction based on the Dirac-Brueckner-Hartree-Fock $G$ matrix starting from a bare nucleon-nucleon interaction is used to explore the $\alpha$-decay half-lives of the nuclei near $N=Z$ line. Specifically, the $\alpha$-nucleus potential is constructed by doubly folding the effective nucleon-nucleon interaction with respect to the density distributions of both the $\alpha$-cluster and daughter nucleus. Moreover, the $\alpha$-cluster preformation factor is extracted by a cluster formation model. It is shown that the calculated half-lives can reproduce the experimental data well. Then, the $\alpha$-decay half-lives that are experimentally unavailable for the nuclei around $N=Z$ are predicted, which are helpful for searching for the new candidates of $\alpha$-decay in future experiments. In addition, by analyzing the proton-neutron correlation energy and two protons-two neutrons correlation energy of $Z=52$ and $Z=54$ isotopes, the $\alpha$-cluster preformation factor evolution with $N$ is explained. Furthermore, it is found that the two protons-two neutrons interaction plays more important role in $\alpha$-cluster preformation than the proton-neutron interaction. Meanwhile, proton-neutron interaction results in the odd-even effect of the $\alpha$-cluster preformation factor.