用深度学习精准预测原子序数≥8核的电荷分布，精度远超传统方法。
Predictions of charge density distributions for nuclei with $Z \geq 8$
- 基于傅里叶-贝塞尔展开，用深度神经网络拟合核结构特征
- 训练与验证集电荷半径均方根误差低至0.0123和0.0198飞米
- 为原子物理与核天体物理提供高精度数据支持
本文构建了一个深度神经网络（DNN），用于精确预测质子数Z≥8的原子核电荷密度分布。模型结合关键核结构特征，通过相对论连续哈特里-博戈留波夫（RCHB）理论计算生成的综合数据集进行训练。采用傅里叶-贝塞尔（FB）级数展开分析电荷密度分布。模型在训练集和验证集上的电荷半径均方根偏差分别为0.0123飞米和0.0198飞米，显著优于原始RCHB计算精度。该高精度模型不仅推动核物理研究进展，还为原子物理、核天体物理等领域的应用提供了关键数据支持。
原文摘要 · Abstract (English)
A deep neural network (DNN) has been developed to accurately predict nuclear charge density distributions for nuclei with proton numbers $Z \geq 8$. By incorporating essential nuclear structure features, the model achieves a significant improvement in predictive accuracy over conventional methods. The charge density distributions are analyzed using a Fourier-Bessel (FB) series expansion, and the DNN is trained on a comprehensive dataset derived from relativistic continuum Hartree-Bogoliubov (RCHB) theory calculations. The model demonstrates exceptional performance, with root-mean-square deviations of 0.0123 fm and 0.0198 fm for charge radii on the training and validation sets, respectively, remarkably surpassing the precision of the original RCHB calculations. Beyond advancing nuclear physics research, this high-precision model provides critical data for applications in atomic physics, nuclear astrophysics, and related fields.
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