Role of Skyrme forces in cluster radioactivity of parent nuclei with even ( A,Z )

Abstract

We investigate the role of different Skyrme forces (SIII, SkI4, and SAMi) in the ground state decay of various radioactive parent nuclei such as Ra, Th, U, and Pu. The daughters of these nuclei are either doubly magic $^{208}\mathrm{Pb}$ or a nearby isotope of Pb. Using spherical choice of cluster and daughter, calculations are performed within the framework of the preformed cluster model (PCM), where the preformation probability ${P}_{0}$ and penetration probability $P$ of decaying fragments are used to obtain the half-lives of cluster emission. The considered forces modify the barrier characteristics and consequently the penetration path, as the scattering potential at the first turning point of the barrier is lowest with the SkI4 force (lowest penetrability) and highest with the SIII force (highest penetrability). However, the preformation probability of decaying clusters is highest for the SkI4 force followed by SAMi and SIII Skyrme forces. To look for the possible role of the spin-orbit effect on the cluster radioactivity, the half-lives of emitted clusters are calculated with and without the inclusion of spin-orbit potential ${V}_{J}$. In addition, the $\ensuremath{\alpha}$-decay half live are also calculated to extract an inclusive picture of the dynamics involved.