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

TL;DR

This work presents a hybrid TabPFN-CPPM framework to infer $\alpha$-particle preformation factors $P_\u03b1$ and to improve $\alpha$-decay half-life predictions. By deriving $P_\u03b1^{exp}$ from CPPM and leveraging TabPFN’s in-context learning on 498 nuclei with nine physical descriptors, the study shows strong shell-structure signatures, odd-even staggering, and a linear $\log_{10}P_\u03b1$ vs. $Q_\u03b1^{-1/2}$ trend, extending Geiger-Nuttall-type systematics to preformation factors. The best TabPFN12 model achieves $\sigma_{RMS}=0.211$, significantly outperforming empirical formulas, and enables reliable extrapolation to superheavy nuclei ($Z=117$--$120$), where $N=184$ emerges as a potential neutron magic number. When TabPFN12 $P_\u03b1$ values are integrated into CPPM, the predicted half-lives show large improvements (e.g., RMS reductions from $\sim$2 to $\sim$0.2–0.8), underscoring the method’s utility for guiding superheavy element synthesis and informing nuclear-structure models.$

Abstract

A hybrid approach combining the Tabular Prior-data Fitted Network (TabPFN) with the Coulomb and Proximity Potential Model (CPPM) is developed to investigate $α$-particle preformation factors $P_α$ and their impact on $α$-decay half-lives. The TabPFN model, trained on 498 nuclei, accurately learns the relationship between the properties of the nuclear structure and $P_α$, achieving a root mean square deviation of $σ_{\mathrm{rms}} = 0.211$. The predicted factors reveal clear odd-even staggering and shell closure effects, and exhibit a linear correlation with $Q_α^{-1/2}$, extending the Geiger-Nuttall systematics. When incorporated into CPPM calculations, the machine learning-based $P_α$ values significantly improve half-life predictions. The capability of the model is demonstrated through predictions for superheavy nuclei ($Z = 117$--120), suggesting $N = 184$ as a potential neutron magic number.

Figures (6)

• Figure 1: Upper panels: Experimental $\alpha$-decay energies $Q_\alpha$(in Mev)for even - even nuclei, plotted against proton number Z (left) and neutron number N (right). Lower panels: Logarithmic values of the $\alpha$-particle preformation factors $\log_{10} P_{\alpha}^{\mathrm{TabPFN12}}$ as functions of Z (left) and N (right).
• Figure 2: From left to right: the empirical logarithms of the $\alpha$-particle preformation factor $\log_{10} P_{\alpha}^{\mathrm{exp}}$, values predicted by the TabPFN12 method $\log_{10} P_{\alpha}^{\mathrm{TabPFN12}}$, and their logarithmic differences $\log_{10} P_{\alpha}^{\mathrm{exp}} - \log_{10} P_{\alpha}^{\mathrm{TabPFN12}}$, each plotted as functions of $Q_{\alpha}^{-1/2}$ (in MeV) for even–even nuclei. The upper row corresponds to nuclei with $N \leqslant 126$, and the lower row to $N > 126$. Linear regression results and residual sum of squares (RSS) values are provided to assess the quality of the fits.
• Figure 3: The $\alpha$-particle preformation factors computed using the TabPFN12 method, plotted as a function of neutron number, for the isotopic chains of Th, Pa, U, Np, and Pu.
• Figure 4: Upper panel: Differences between experimental and theoretical half-lives for 498 nuclei within the CPPM framework, showing results both with and without inclusion of the $P_{\alpha}^{\mathrm{TabPFN12}}$ preformation factor. Lower panel: Corresponding deviations for the additional set of 41 nuclei.
• Figure 5: Upper panel: Predicted $\alpha$-particle preformation factors $P_{\alpha}^{\mathrm{TabPFN12}}$ for isotopic chains of $Z = 117$ and 118. Lower panel: Corresponding predictions for $Z = 119$ and 120 isotopic chains.