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 $\sigma_{ \mathrm{ rms}} = 0.211$. The predicted factors reveal clear odd-even staggering and shell closure effects, and exhibit linear correlations with both $Q_{ \alpha}^{ -1/2}$ and the fragmentation potential $V_{ \mathrm{ frag}}$. 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.
Categories: nucl-th