Alpha decay of heavy and super heavy nuclei with a generalized electrostatic potential

The emission of $ \alpha $ clusters represents the favored decay mode for most unstable medium mass nuclei, heavy nuclei, and super-heavy nuclei. Since its first experimental observation by Rutherford [1,2], it naturally became one of the standard tools for the study of nuclear structures and reactions and the exclusive way for the identification of new super-heavy nuclei. Moreover, the theoretical interpretation of $ \alpha $ decay as a quantum tunneling effect through a nuclear Coulomb barrier [3] represented a real breakthrough for quantum physics in general, by validating its hypotheses experimentally. The basic experimental observables related to this phenomenon are the $ \alpha $ decay energy $ Q_{\alpha} $ and the associated half-lives $ T_ {\frac {1}{2}} $ . The first notable success of treating $ \alpha $ decay as a semiclassical one-dimensional quantum tunneling process lead to simple but extremely precise correlations relating half-lives, $ Q_{\alpha} $ values, and nucleon numbers through a WKB estimation of the barrier penetration probability. The first correlation of this type was proposed by Geiger and Nuttall [4], which became the basis for various continuously improved empirical formulas for $ \log_{10}T_{\frac {1}{2}} $