Systematic Study on the $\alpha$-particle preformation factor in the theory of $\alpha$-decay based on the Tabular Prior-data Fitted Network (TabPFN)

A hybrid approach combining the Tabular Prior-data Fitted Network (TabPFN) with the Coulomb and Proximity Potential Model (CPPM) is developed to investigate $\alpha$-particle preformation factors $P_{\alpha }$ and their impact on $\alpha$-decay half-lives. The TabPFN model, trained on 498 nuclei, accurately learns the relationship between nuclear structure properties and $P_{\alpha }$, achieving a root mean square deviation of ${\sigma }_{\mathrm{r}\mathrm{m}\mathrm{s}}=0.211$. The predicted factors reveal clear odd-even staggering and shell closure effects, and exhibit linear correlations with both $Q_{\alpha }^{-1\mathrm{/}2}$ and the fragmentation potential $V_{\mathrm{f}\mathrm{r}\mathrm{a}\mathrm{g}}$. When incorporated into CPPM calculations, the machine-learning-based $P_{\alpha }$ values significantly improve half-life predictions. Similar improvements are also obtained when deformation effects are included in the potential barrier description. The capability of the model is further demonstrated through predictions for superheavy nuclei ($Z=117$–120), suggesting $N=184$ as a potential neutron magic number.