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

The $\alpha$ decay provides valuable constraints on nuclear structure and plays an essential role in identifying heavy and superheavy nuclei. We study $\alpha$-decay half-lives of 178 even-even nuclei within a semi-classical WKB framework using a phenomenological Woods-Saxon $\alpha$-nucleus potential. The potential depth is determined by imposing the Bohr-Sommerfeld quantization condition (BSQC), ensuring a physically consistent description of the quasibound $\alpha$-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 $\alpha$ decay.