Systematics of alpha decay half-lives within the position-dependent mass formalism

In this paper, we present a new study about $\alpha$ decay process in the framework of the quantum concept, namely: the position dependent mass formalism. Such a study allowed us to obtain a new generalized formula for $\alpha$ decay half-lives which enables us to rebuild the majority of the formulas existing in the literature. Moreover, from this generalized formula, we derived two new practical ones. We have tested these two latter on 397 nuclei (52<Z<118). By comparing our obtained results with those from the majority of semi-empirical formulas in the literature, it comes out that one of these two new proposed formulas is the most precise one inasmuch as it presents the lowest r.m.s deviation in respect to the experimental data particularly for even-even nuclei. Based on this new formula, we make predictions for some super-heavy nuclei.