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

TL;DR

The paper addresses accurate prediction of $α$-decay half-lives in superheavy nuclei by integrating nonlocal dynamical effects into the Coulomb and Proximity Potential Model with a Cluster Formation Model-based preformation factor, and by calibrating model residuals using a Bayesian Neural Network. The approach combines physical modeling (CPPM, nonlocality, and UDL variants) with data-driven calibration (BNN) and interprets feature importance via SHAP, revealing $Q_{α}$ as the dominant driver and highlighting shell effects near $N=184$ in extrapolated isotopes $Z=118$ and $Z=120$. Quantitatively, nonlocal corrections reduce RMSE by about 32% compared to the base CPPM, while BNN calibration yields larger gains (up to ≈48% when combined with nonlocality), with additional small improvements from including deformation $β_2$. The results confirm the method’s fidelity to the Geiger–Nuttall law and its capacity to extrapolate to the superheavy region, underscoring the value of combining physically informed models with Bayesian uncertainty-aware learning for nuclear decay predictions.

Abstract

We combine nonlocal effects with Bayesian Neural Network (BNN) methods to enhance the prediction accuracy of $α$ 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 $β_2$) on machine learning predictions. Through Shapley Additive Explanations (SHAP), we conducted a quantitative comparison of six input features within the BNN, revealing that the $α$ decay energy $Q_α$ is the primary driving factor affecting the half-life $T_{1/2}$. Leveraging the remarkable extrapolation ability of the BNN, we successfully predicted the $α$ 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 $α$ decay half-lives and $Q_α$ values satisfy the Geiger-Nuttall (G-N) linear relationship. This result further confirms the predictive reliability of the proposed model. Keywords: $α$ decay, half-lives, nonlocal effects, Bayesian Neural Network, Coulomb and proximity potential model

Figures (5)

• Figure 1: The impact of nonlocal effects on tunneling calculations is illustrated using the example of $^{184m}_{78}Pt$$\alpha$ decay. In panel (a), the effective reduced mass $\mu$ is presented considering nonlocal effects. Panel (b) compares the barrier penetration integral function $f(r)$: the reduced mass $\mu$ (blue curve, $\rho_{s} = -0.615$) versus $\mu_{0}$ (red curve, $\rho_{s} = 0$).
• Figure 2: The figure displays the importance ranking of four input features obtained using the SHAP toolkit. Each row represents a feature, with the horizontal axis showing its SHAP value, which reflects the feature's significance in the specific prediction. Each point corresponds to a sample, and the color of the points indicates the feature value, with red representing high values and blue representing low values.
• Figure 3: $\alpha$ decay half-lives of isotopes with atomic numbers $Z=118$ and $Z=120$ predicted using the BNN method. Herein, black squares and red dots correspond to $Z = 118$ and $Z = 120$, respectively; the horizontal axis denotes the neutron number $N$, and the vertical axis represents the logarithm of the half-life, $\log_{10}T_{1/2}$; three mass tables (RCHB, WS4, FRDM) are employed in this figure.
• Figure 4: G-N plots of $\alpha$ decay for Z=118 and Z=120 isotopes predicted by the BNN method.
• Figure 5: Universal curves of $\alpha$ decay half-lives for isotopes with atomic numbers $Z=118$ and $Z=120$ versus negative logarithm of penetrability ($-\ln$P) predicted using BNN method.