Analytical penetration probability including the centrifugal potential: An improved Buck--Merchant--Perez model for alpha-decay half-lives

Abstract

We derive a closed-form, non-perturbative WKB penetration formula for alpha-decay that explicitly incorporates the centrifugal potential within the Buck--Merchant--Perez (BMP) cluster model. The centrifugal term is shown to enhance the hindrance by effectively enlarging the barrier width: it pushes the outer turning point outward and, via the Bohr--Sommerfeld quantization condition, shifts the inner turning point inward. Building on this analytical result, we further develop an improved BMP model in which the nuclear potential depth is expressed as a unified four-parameter formula that simultaneously encodes shell corrections, odd-even pairing effects, and orbital-angular-momentum dependence. For 534 ground-state-to-ground-state alpha decays spanning Z = 60--118, the root-mean-square deviation of log base 10 T1/2 is reduced to 0.267, representing a 57% improvement over the original constant-depth BMP model (0.615), with robust performance for both favored (0.188) and unfavored (0.398) transitions. The framework is further applied to predict the half-lives of hitherto-unmeasured nuclei in the region Z = 117--120, providing quantitative benchmarks for future experimental investigations.