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It is common to study the strong decay of a heavy nucleus as a tunnelingphenomenon where the $\alpha$ ($^4$He) or a light nuclear cluster tunnelsthrough the Coulomb barrier formed by its interaction with the heavier daughternucleus. The position and width of the Coulomb barrier are determined by thetotal interaction potential between the two daughter nuclei. We examine theeffects of including nonlocality and deformation in the interaction potentialby calculating the half-lives, $t_{1/2}$, and thereby phenomenologicalpreformation factors of several nuclei which have the possibility of decayingby emitting either an $\alpha$ or a light nuclear cluster. The effect ofdeformation manifests itself by a decrease in $t_{1/2}$ for all the decaysstudied. The effect of nonlocality is studied within two different models ofthe 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 allhalf-lives studied. Though the decrease is larger due to the Perey-Buckpotential, half-lives evaluated using the Mumbai potential show a strongsensitivity to the $l$ value in the decay. This feature of the $\alpha$ andcluster decay half-lives can provide a complementary tool in addition toscattering data which are more commonly used to fix the parameters of anonlocal potential in literature.

Manifestation of deformation and nonlocality in $\alpha$ and cluster decay