Calculation of $\alpha$-decay half-lives for isotopes around $N=Z$ using different proximity-type potentials

Abstract

Within the framework of 16 different versions of proximity potentials, we study the alpha decay half-lives of 21 probable isotopes of nuclei around $N=Z$ in the range of $52\le Z\le 56$. The obtained results show that the theoretical half-lives of the Prox. 81 (set III) and Prox. 88 potential models are in very close agreement with the available experimental data. For comparison, the validity of the generalized liquid drop model (GLDM) and effective liquid drop model (ELDM) are also evaluated in reproducing the experimental data of alpha radioactivity half-lives. On the basis of the isotopic dependence of the Coulomb potential barrier and the released energy $Q_{\alpha }$, we discuss the variation in the penetration probability of $\alpha$-particle and alpha decay half-lives with neutron content. The validity of the Geiger–Nuttall (GN) law is examined for $\alpha$ transitions from the ground state of the selected parent nuclei. The values produced by the present proximity potentials are compared with those obtained by some of the well-known empirical and semi-empirical formulae, including Royer, SemFIS (semi-empirical relationship based on fission theory), Akrawy, MRenB, YQZR, MYQZR, and AKRA. The computed standard deviations of the calculated half-lives in comparison with the experimental data suggest that the SemFIS formula produces the lowest standard deviation among the different formulae for alpha decay of the present nuclei. The present approaches are also employed to predict the alpha radioactivity half-lives for parent nuclei at around $N=Z$ whose the experimental data are not available for them.