Different models for the nonlocal description of the nuclear interaction are compared through a study of their effects on the half-lives of radioactive nuclei decaying by the emission of alpha particles. The half-lives are evaluated by considering a pre-formed alpha particle ($^4$He nucleus) which tunnels through the Coulomb barrier generated by its interaction with the daughter nucleus. An effective potential obtained from a density dependent double folding strong potential between the alpha and the daughter nucleus within the nonlocal framework is found to decrease the half-lives as compared to those in the absence of nonlocalities. Whereas the percentage decrease within the older Perey-Buck and S~ao Paulo models ranges between 20 to 40% for medium to heavy nuclei, a recently proposed effective potential leads to a decrease of only 2 - 4 %. In view of these results, we provide a closer examination of the approximations used in deriving the local equivalent potentials and propose that apart from the scattering data, the alpha decay half-lives could be used as a complementary tool for constraining the nonlocality models.
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