Systematic Study of Proton, Two-Proton, Alpha, and Cluster Radioactivity Half-Lives based on the Deformed Gamow-like Model and Tabular Prior-data Fitted Network ($\mathrm{TabPFN}$)

Abstract

A hybrid framework combining the deformed Gamow-like model ($\mathrm{DGLM}$) with the Tabular Prior-data Fitted Network ($\mathrm{TabPFN}$) is developed to improve half-life predictions for two-proton emission, proton emission, $\alpha$ decay, and cluster radioactivity. A total of 583 radioactive nuclei are investigated, including 17 two-proton emitters, 42 proton emitters, 498 $\alpha$ emitters, and 26 cluster emitters. Among the four considered models, ${\mathrm{DGLM}}^b+\mathrm{TabPFN}$ achieves the best overall performance, with ${\sigma }_{\mathrm{RMS}}=0.423$, corresponding to an improvement of approximately $82.2\%$ over ${\mathrm{DGLM}}^b$. The model parameters are optimized for each decay mode using the least-squares method. After introducing $\mathrm{TabPFN}$, the prediction errors for proton emission and $\alpha$ decay are reduced by approximately $80.6\%$ and $87.6\%$, respectively. For $\alpha$ decay, the training, test, and overall RMSEs are 0.208, 0.305, and 0.240, indicating good generalization capability without evident overfitting. The model also reproduces the systematic evolution of $\alpha$-decay half-lives and the shell-closure effect around $N=126$. These results demonstrate that combining $\mathrm{DGLM}$ with $\mathrm{TabPFN}$ significantly improves the accuracy and robustness of radioactive-decay half-life predictions while retaining the physical interpretability of the original model.

Comments: 15 pages, 9 figure, 8 tables