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<p>Recently, machine learning has become a powerful tool for predicting nuclear charge radius <i>R</i><sub>C</sub>, providing novel insights into complex physical phenomena. This study employs a continuous Bayesian probability (CBP) estimator and Bayesian model averaging (BMA) to optimize the predictions of <i>R</i><sub>C</sub> from sophisticated theoretical models. The CBP estimator treats the residual between the theoretical and experimental values of <i>R</i><sub>C</sub> as a continuous variable and derives 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 the unique strengths of each model. In global optimization, the CBP estimator improved the predictive accuracy of the three theoretical models by approximately 60%. The extrapolation analyses consistently achieved 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 <i>R</i><sub>C</sub> of the Ca and Sr isotope chains. The studies in this paper propose an efficient method to accurately describe <i>R</i><sub>C</sub> of unknown nuclei, with potential applications in research on other nuclear properties.</p>

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Continuous Bayesian probability estimator in predictions of nuclear charge radii

  • 期刊论文

  • 发表日期：

    2025年8月30日

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  • Jian Liu,
  • Kai-Zhong Tan,
  • Lei Wang,
  • Wan-Qing Gao,
  • Tian-Shuai Shang,
  • Jian Li,
  • Chang Xu

摘要

Recently, machine learning has become a powerful tool for predicting nuclear charge radius RC, providing novel insights into complex physical phenomena. This study employs a continuous Bayesian probability (CBP) estimator and Bayesian model averaging (BMA) to optimize the predictions of RC from sophisticated theoretical models. The CBP estimator treats the residual between the theoretical and experimental values of RC as a continuous variable and derives 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 the unique strengths of each model. In global optimization, the CBP estimator improved the predictive accuracy of the three theoretical models by approximately 60%. The extrapolation analyses consistently achieved 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 RC of the Ca and Sr isotope chains. The studies in this paper propose an efficient method to accurately describe RC of unknown nuclei, with potential applications in research on other nuclear properties.