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Nuclear isospin asymmetry in $α$ decays of heavy nuclei

The effects of nuclear isospin asymmetry on $α$ decay lifetimes of heavy nuclei are investigated within various phenomenological models of nuclear potential for the $α$ particle. We consider the widely used simple square well potential and Woods-Saxon potential, and modify them by including an isospin asymmetry term. We then suggest a model for the potential of the $α$ particle motivated by a microscopic phenomenological approach of the Skyrme force model, which naturally introduce the isospin dependent form of the nuclear potential for the $α$ particle. The empirical $α$ decay lifetime formula of Viola and Seaborg is also modified to include isospin asymmetry effects. The obtained $α$ decay half-lives are in good agreement with the experimental data and we find that including the nuclear isospin effects somehow improves the theoretical results for $α$ decay half-lives. The implications of these results are discussed and the predictions on the $α$ decay lifetimes of superheavy elements are also presented.