Bayesian optimization and nonlocal effects method for $\alpha$ decay of superheavy nuclei based on CPPM

We combine nonlocal effects with Bayesian Neural Network (BNN) methods to enhance the prediction accuracy of $\alpha$ decay half-lives. The results indicate that accounting for nonlocal effects significantly impacts the half-life calculations, while the BNN method markedly improves prediction accuracy and demonstrates strong extrapolation capabilities. Furthermore, we discuss the impact of nuclear deformation (the quadrupole deformation factor $\beta_2$) on machine learning predictions. Through Shapley Additive Explanations (SHAP), we conducted a quantitative comparison of six input features within the BNN, revealing that the $\alpha$ decay energy $Q_\alpha$ is the primary driving factor affecting the half-life $T_{1/2}$. Leveraging the remarkable extrapolation ability of the BNN, we successfully predicted the $\alpha$ decay half-lives of the isotope chain ($Z=118, 120$), uncovering a significant shell effect at neutron number $N=184$. For the isotopic chains ($Z=118, 120$), the predicted $\alpha$ decay half-lives and $Q_{\alpha}$ values satisfy the Geiger-Nuttall (G-N) linear relationship. This result further confirms the predictive reliability of the proposed model. Keywords: $\alpha$ decay, half-lives, nonlocal effects, Bayesian Neural Network, Coulomb and proximity potential model