Analytical penetration probability including the centrifugal potential: An improved Buck--Merchant--Perez model for alpha-decay half-lives
arXiv:2607.12238
The paper derives an analytical WKB formula for alpha‑decay that includes the centrifugal potential, and uses it to improve the Buck‑Merchant‑Perez cluster model for predicting alpha‑decay half‑lives across heavy nuclei.
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.
17 pages,5 figures