Preformation probability inside α emitters around the shell closures Z = 50 and N = 82

The preformation of an α-particle as a distinct entity inside the α-emitter is the first move towards α-decay. We investigate the α-particle preformation probability (S _α) in ordinary and exotic α-decays. We consider favored and unfavored decays at which the α-emitters and the produced daughter nuclides are in their ground or isomeric states. The study of 244 α-decay modes with $52⩽Z⩽81$ and $53⩽N⩽112$ is accomplished using the preformed cluster model. The preformation probabilities were estimated from the experimental half-lives and the computed decay widths based on the Wentzel–Kramers–Brillouin tunneling penetrability and knocking frequency, and the Skyrme-SLy4 interaction potential. We found that the favored α-decay mode from a ground state to an isomeric state shows larger α-preformation probability than the favored and unfavored decays of the same isotope but from isomeric to ground states. The favored decay mode from isomeric- to ground-state exhibits rather less S _α relative to the other decay modes from the same nuclide. The favored decay modes between two isomeric states tend to yield larger S _α and less partial half-life compared with the favored and unfavored decays from the same nuclides but between two ground states. For the decays involving two ground states, the preformation probability is larger for the favored decay modes than for the unfavored ones. The unfavored α-decay modes from ground- to isomeric-states are rare. The unfavored decay modes from isomeric- to ground-states show less S _α than that for the favored decays from the ground states of the same emitters. The unfavored α-decay modes between two isomeric states exhibit larger S _α than the other α-decay modes from the same isomers. (paper)