α-decay widths from two-potential approaches and WKB prefactors
Abstract
The accurate calculation of α-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 α preformation effects. We benchmark single-particle α-decay widths across 161 even-even nuclei (Ap=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 cos2→ 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 α-decay tunneling analysis and provides a clean reference for isolating preformation and structure effects in future studies.
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BibTeX
@misc{nga2026αdecay,
title = {{$α$-decay widths from two-potential approaches and WKB prefactors}},
author = {Nguyen Thi Huyen Nga and Le Quoc Thai and Chau Van Tao and Le Hoang Chien and Nguyen Tri Toan Phuc},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00131},
eprint = {2611.00131},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00131},
}
RIS
TY - UNPB
TI - α-decay widths from two-potential approaches and WKB prefactors
AU - Nguyen Thi Huyen Nga
AU - Le Quoc Thai
AU - Chau Van Tao
AU - Le Hoang Chien
AU - Nguyen Tri Toan Phuc
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00131
UR - https://arxiv.org/abs/2611.00131
AB - The accurate calculation of α-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 α preformation effects. We benchmark single-particle α-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→ 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 α-decay tunneling analysis and provides a clean reference for isolating preformation and structure effects in future studies.
ER -