A global potential constrained by the Bohr-Sommerfeld quantization condition for $α$-decay half-lives of even-even nuclei

TL;DR

This study addresses global α-decay systematics by constraining a phenomenological Woods-Saxon α–nucleus potential with the Bohr-Sommerfeld quantization condition within a semi-classical WKB framework. It demonstrates that a BSQC-determined potential depth and a globally fitted depth yield α-decay half-lives in good agreement with experiment, with rms deviations around 0.25 in the decimal logarithm. The fitted approach substantially reduces computational costs for large-scale surveys while preserving accuracy comparable to direct BSQC calculations and competitive with semi-microscopic double-folding potentials. Focused on 178 even-even nuclei and ground-state transitions, the work lays groundwork for scalable α-decay descriptions and points to future extensions to odd-A/odd-odd systems, deformation effects, and explicit preformation dynamics.

Abstract

The $α$ decay provides valuable constraints on nuclear structure and plays an essential role in identifying heavy and superheavy nuclei. We study $α$-decay half-lives of 178 even-even nuclei within a semi-classical WKB framework using a phenomenological Woods-Saxon $α$-nucleus potential. The potential depth is determined by imposing the Bohr-Sommerfeld quantization condition (BSQC), ensuring a physically consistent description of the quasibound $α$-daughter system. To facilitate large-scale calculations, a global parametrization of the BSQC-constrained potential depth is constructed. The resulting half-lives reproduce experimental data with comparable accuracy for both the direct BSQC approach and the fitted prescription, providing a first step toward a global and computationally efficient description of $α$ decay.

Figures (4)

• Figure 1: Depth $V_0$ of the WS potential determined from the BSQC for 178 even-even nuclei. These values are used to construct the fitted parametrization given in Eq. \ref{['eq:V0_fit']}.
• Figure 2: Nuclide-chart distribution of the decimal logarithmic deviation $\log\left(T_{1/2}^{\mathrm{Cal}}/T_{1/2}^{\mathrm{Exp}}\right)$ between calculated and experimental $\alpha$-decay half-lives, plotted as a function of the neutron and proton numbers $(N, Z)$ of the parent nuclei. The color scale indicates the magnitude of the deviation. The results are obtained using the WS potential depth $V_0$ determined from the BSQC in Eq. \ref{['eq:bsqc']} (a) and from the fitted parametrization in Eq. \ref{['eq:V0_fit']} (b). For comparison, results calculated with the semi-microscopic DF potential based on the CDM3Y3 interaction from Ref. chien2022 are shown in (c). The dotted lines indicate the magic numbers $N=126$ and $Z=82$. Experimental data are taken from Ref. kondev2021.
• Figure 3: The rms deviation $\chi$ between the decimal logarithms of calculated and experimental $\alpha$-decay half-lives as a function of the diffuseness parameter $a_0$. The radius parameter is fixed at $r_0 = 1.27$ fm.
• Figure 4: Same as Figure \ref{['fig:a0']} but for the function of the radius parameter $r_0$. The diffuseness parameter is fixed at $a_0 = 0.64$ fm.