Phenomenological studies for α-decay process within position-dependent effective mass

In this work, we present a new phenomenological study of the favored and unfavored α-decay process within the framework of position-dependent effective mass (PDEM) and the WKB approximation. Our approach integrates the quantum concept of PDEM into a simplified model while explicitly incorporating the centrifugal barrier effect, which arises from the transfer of angular momentum of the emitted particle. This contribution is essential for analyzing even-odd, odd-even and odd-odd nuclei. By deriving the deformed Schrödinger equation with this additional term, we refine the expression for the α-decay half-life. The proposed formula has been tested on 397 nuclei, classified into four configurations: even-even, even-odd, odd-even, and odd-odd. The results show excellent agreement with experimental data across all cases. Furthermore, we emphasize that the deformation parameter β, introduced through the PDEM framework, is not merely an adjustable fitting parameter but is intrinsically linked to the underlying structure of the model.