Collective clusterization approach to investigate the relevance of deformation effects in Sn radioactivity

Abstract

The role of deformations and orientations is studied in cluster decays of various radioactive nuclei leading to doubly magic 100Sn or 132Sn daughter nucleus, using the preformed cluster model (PCM). This model treats the cluster emission process via tunnelling across the potential barrier, the cluster/fragment being preformed with a relative probability $ P_0$. With the incorporation of deformation and orientation effects, the fragmentation potential, the penetration path and related barrier characteristics get significantly modified, due to which both the preformation probability $ P_0$ and penetrability P of the emitting cluster get influenced. The calculated half-lives of the decaying clusters calculated using PCM are found to be within the upper limits of the present experiments. The influence of deformations and orientations on Sn radioactivity is also seen in terms of various barrier characteristics such as barrier modification, barrier height, etc. Moreover, the role of different nuclear proximity potentials, i.e., Prox 77, Prox 88 and Prox 00, is analyzed in the context of potential energy surfaces (PES) in the ground-state decay of parent nucleus. The behavior of PES is explored including, as well as without including, the shell corrections in the binding energies, which in turn help to explore the importance of doubly magic closed shell configuration of daughter and cluster nuclei. The possible role of higher order multipole deformations (i.e., up to $ \beta_{4i}$) is also analyzed in view of the fragmentation path and barrier tunnelling characteristics.