Half-lives and cluster preformation factors for various cluster emissions in trans-lead nuclei

Abstract

The generalized density-dependent cluster model (GDDCM) is extended to study cluster radioactivity in even-even and odd-$A$ nuclei decaying to the doubly magic nucleus $^{208}\mathrm{Pb}$ or its neighboring nuclei. The microscopic cluster-daughter potential is numerically constructed in the double-folding model with M3Y nucleon-nucleon interactions plus proton-proton Coulomb interactions. Instead of the WKB barrier penetration probability, the exact solution of the Schr\odinger equation with outgoing Coulomb wave boundary conditions is presented. The cluster preformation factor is well taken into account based on some available experimental cases. The calculated half-lives are found to be in good agreement with the experimental data. This indicates that a unified description of $\ensuremath{\alpha}$ decay and cluster radioactivity has been achieved by the GDDCM. Predictions of cluster emission half-lives are made for promising emitters, which may guide future experiments.