基于形变类Gamow模型与表格先验数据拟合网络（$\mathrm{TabPFN}$）的质子、双质子、α及团簇放射性半衰期系统性研究
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 ($\mathrm{TabPFN}$)
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- College of Physics and Technology, Kunming University（昆明大学物理与技术学院）
- School of Physics and Information Engineering, Zhaotong University（昭通大学物理与信息工程学院）
- Key Laboratory of Economic System Simulation of Guizhou Province, Guizhou University of Finance and Economics（贵州省经济系统模拟重点实验室，贵州财经大学）
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中文总结 AI 辅助
本研究将形变类Gamow模型与TabPFN结合，预测583个核素的衰变半衰期，误差降低约82%，并保持物理可解释性。
中文摘要 AI 辅助
开发了一种将形变类Gamow模型（$\mathrm{DGLM}$）与表格先验数据拟合网络（$\mathrm{TabPFN}$）相结合的混合框架，以提高双质子发射、质子发射、$\alpha$衰变和团簇放射性的半衰期预测精度。共研究了583个放射性核素，包括17个双质子发射体、42个质子发射体、498个$\alpha$发射体和26个团簇发射体。在考虑的四种模型中，$\mathrm{DGLM}^{b}+\mathrm{TabPFN}$取得了最佳整体性能，其$\sigma_{\mathrm{RMS}}=0.423$，相较于$\mathrm{DGLM}^{b}$提高了约82.2%。模型参数通过最小二乘法针对每种衰变模式进行优化。引入$\mathrm{TabPFN}$后，质子发射和$\alpha$衰变的预测误差分别降低了约80.6%和87.6%。对于$\alpha$衰变，训练集、测试集和整体的均方根误差（RMSE）分别为0.208、0.305和0.240，表明模型具有良好的泛化能力，且无明显过拟合。该模型还再现了$\alpha$衰变半衰期的系统演化以及$N=126$附近的壳闭合效应。这些结果表明，将$\mathrm{DGLM}$与$\mathrm{TabPFN}$相结合，在保留原始模型物理可解释性的同时，显著提高了放射性衰变半衰期预测的准确性和鲁棒性。
英文摘要
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, $α$ decay, and cluster radioactivity. A total of 583 radioactive nuclei are investigated, including 17 two-proton emitters, 42 proton emitters, 498 $α$ emitters, and 26 cluster emitters. Among the four considered models, $\mathrm{DGLM}^{b}+\mathrm{TabPFN}$ achieves the best overall performance, with $σ_{\mathrm{RMS}}=0.423$, 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 $α$ decay are reduced by approximately $80.6\%$ and $87.6\%$, respectively. For $α$ 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 $α$-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.
