AI 中文总结
研究利用核结合能数据为电荷半径建模，提出单参数公式$\mathrm{BECR}_\mathrm{1p}$，结合能关联与结构修正，在实验电荷半径数据上验证，经多步修正及AKRR处理降低偏差，并用此公式预测大量核的电荷半径。
AI 中文摘要
核结合能和电荷半径源于相同的基础物理：饱和性、同位旋依赖性、壳层结构和形变。结合能数据为电荷半径建模提供自然约束。我们提出一个单参数电荷半径公式（$\mathrm{BECR}_\mathrm{1p}$），它将结合能关联与局部结构修正相结合。在一组893个实验电荷半径上，仅宏观的BECR项就能以0.0345 fm的均方根偏差再现主要电荷半径尺度；加入壳层、奇偶、有限尺寸和形变修正后，BECR1p的均方根偏差进一步降至0.0138 fm。应用于残差的各向异性核岭回归（AKRR）进一步将留一法交叉验证均方根偏差降至约0.0081 fm。我们用该公式预测了核素图上11205个核的电荷半径。
英文摘要
Nuclear binding energies and charge radii stem from the same underlying physics: saturation, isospin dependence, shell structure, and deformation. Binding-energy data therefore provide a natural constraint for charge-radius modeling. We propose a one-parameter charge-radius formula ($\mathrm{BECR}_\mathrm{1p}$) that combines binding-energy correlations with local structural corrections. On a curated set of 893 experimental charge radii, the macroscopic BECR term alone reproduces the leading charge-radius scale with a root-mean-square deviation (RMSD) of 0.0345 fm; adding shell, odd--even, finite-size, and deformation corrections further reduces the RMSD of BECR1p to 0.0138 fm. An anisotropic kernel ridge regression (AKRR) applied to the residuals further lowers the leave-one-out cross-validation RMSD to about 0.0081 fm. We use the formula to predict charge radii for 11205 nuclei across the nuclear chart.
Comments15 pages, 5 figures, 1 table
