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

TL;DR

The paper addresses α-decay near the $N=Z$ line by employing a microscopic DBHF $G$-matrix-based $n$-$n$ interaction folded with $ ho_\alpha$ and $\rho_d$ to form the α–nucleus potential, and by using a cluster formation model to extract the α preformation factor $P_\alpha$. It combines a double-folding approach with a density-dependent effective interaction and Bohr-Sommerfeld quantization to determine the renormalization factor and turning points, then computes the decay width and half-life via a WKB-like expression. The results show that the DBHF-based calculations reproduce experimental $T_{1/2}$ data with higher accuracy than GLDM, and they provide predictions for unmeasured decays in Te, I, Xe, Cs, and Ba isotopes around $N=Z$. A correlative analysis using $E_{p-n}$ and $E_{2p-2n}$ indicates that $2p$-$2n$ interactions dominate α preformation and that odd-even staggering arises from $E_{p-n}$, offering insight into the microscopic origin of α clustering. The framework advances understanding of α-clustering near the $N=Z$ line and offers guidance for future experiments and potential extension to other decay modes such as cluster and proton radioactivity.

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 $α$-decay half-lives of the nuclei near $N=Z$ line. Specifically, the $α$-nucleus potential is constructed by doubly folding the effective nucleon-nucleon interaction with respect to the density distributions of both the $α$-cluster and daughter nucleus. Moreover, the $α$-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 $α$-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 $α$-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 $α$-cluster preformation factor evolution with $N$ is explained. Furthermore, it is found that the two protons-two neutrons interaction plays more important role in $α$-cluster preformation than the proton-neutron interaction. Meanwhile, proton-neutron interaction results in the odd-even effect of the $α$-cluster preformation factor.

Figures (3)

• Figure 1: (Color online) Total interaction potential $V(R)$ (red solid curve), nuclear potential $V_{N}\left( R \right )$ (green dot-dash curve) and Coulomb potential $V_{c}\left( R \right )$ (blue dash curve) for $^{112}$Xe, respectively.
• Figure 2: (Color online) The logarithm hindrance factors $\log_{10}{HF}$ for the nuclei around $N=Z$. The red squares and blue triangles represent the results from the DBHF and the GLDM Ghar22, respectively.
• Figure 3: (Color online) (a) The $P_{\alpha }$ values of $Z=52$ and $Z=54$ isotopes versus $N$. (b) Same as (a), but for the proton-neutron correlation energy $E_{p-n}$ and two protons-two neutrons correlation energy $E_{2p-2n}$, respectively.