$\alpha$-decay widths from two-potential approaches and WKB prefactors

Abstract

The accurate calculation of $\alpha$-decay widths can be obtained with several equivalent descriptions of the Gurvitz-Kalbermann two-potential approach (TPA) or a semiclassical WKB description having both correct barrier penetrability and consistent inner-state normalization prefactor. This prefactor, which is related to the assault frequency, is implemented in several ways in the literature, producing systematically different results that can be mistaken for $\alpha$ preformation effects. We benchmark single-particle $\alpha$-decay widths across 161 even-even nuclei ($A_p=144$--$252$) using several TPA descriptions and WKB calculations with four common prefactors, employing a Woods-Saxon potential fixed by the quantization-constrained parameter method. The TPA formulas agree to within a few parts in $10^{-8}$, highlighting their robustness. Among semiclassical prefactors, only the widely used round-trip (RT) approximation closely reproduces the TPA widths to within a few percent. An Airy-function analysis reveals this ${\cos }^2\to 1/2$ averaged WKB prefactor is the correct leading-order semiclassical normalization of the exact quasibound state, clarifying the counterintuitive empirical observations associated with the WKB prefactors. Our benchmark identifies the WKB prefactor appropriate for $\alpha$-decay tunneling analysis and provides a clean reference for isolating preformation and structure effects in future studies.

arXiv comment4 figures, 1 table