Continuous Bayesian probability estimator in predictions of nuclear charge radii

分类： 物理学 >> 核物理学 提交时间： 2025-01-09

Tan, Mr. Kaizhong Wang, Ms. Lei Gao, Ms. Wanqing Shang, Mr. Tian-shuai Li, Dr. Jian Xu, Prof. Chang Liu, Dr. Jian

摘要： Recently, machine learning has become a powerful tool for predicting nuclear charge radius $R_{\mathrm{C}}$, providing novel insights into complex physical phenomena. This study employs the continuous Bayesian probability (CBP) estimator and the Bayesian model averaging (BMA) to optimize the predictions of $R_{\mathrm{C}}$ from sophisticated theoretical models. The CBP estimator treats the residual between the theoretical and experimental values of $R_{\mathrm{C}}$ as a continuous variable, deriving its posterior probability density function (PDF) from Bayesian theory. The BMA method assigns weights to models based on their predictive performance for benchmark nuclei, thereby accounting for each model's unique strengths. In global optimization, the CBP estimator improves the predictive accuracy of the three theoretical models by about 60\%. In extrapolation analyses, it consistently achieves an improvement rate of approximately 45\%, demonstrating the robustness of the CBP estimator. Furthermore, the combination of the CBP and BMA methods reduces the standard deviation to below 0.02 fm, effectively reproducing the pronounced shell effects on $R_{\mathrm{C}}$ of the Ca and Sr isotope chains. The studies in this paper propose an efficient way to accurately describe $R_{\mathrm{C}}$ of unknown nuclei, with potential applications to research on other nuclear properties.

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