Manifestation of deformation and nonlocality in $α$ and cluster decay

Abstract: It is common to study the strong decay of a heavy nucleus as a tunneling phenomenon where the $\alpha$ ($<sup>4$He) or a light nuclear cluster tunnels through the Coulomb barrier formed by its interaction with the heavier daughter nucleus. The position and width of the Coulomb barrier are determined by the total interaction potential between the two daughter nuclei. We examine the effects of including nonlocality and deformation in the interaction potential by calculating the half-lives, $t_{1/2}$, and thereby phenomenological preformation factors of several nuclei which have the possibility of decaying by emitting either an $\alpha$ or a light nuclear cluster. The effect of deformation manifests itself by a decrease in $t_{1/2}$ for all the decays studied. The effect of nonlocality is studied within two different models of the nuclear potential: the energy-independent but angular momentum ($l$) dependent Mumbai (M) potential and the energy-dependent Perey-Buck (PB) potential. The nonlocal nuclear interaction leads to a decrease in all half-lives studied. Though the decrease is larger due to the Perey-Buck potential, half-lives evaluated using the Mumbai potential show a strong sensitivity to the $l$ value in the decay. This feature of the $\alpha$ and cluster decay half-lives can provide a complementary tool in addition to scattering data which are more commonly used to fix the parameters of a nonlocal potential in literature.