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arXiv · 2607.15064

Extracting nuclear charge radii from binding energies: a single-parameter empirical formula with structural corrections

Pengfei Ma·Minghui Hu·Kai Ren·Junlong Tian·Cheng Li
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Abstract

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.

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Pengfei Ma, Minghui Hu, Kai Ren, Junlong Tian, Cheng Li. 2026-07-16. Extracting nuclear charge radii from binding energies: a single-parameter empirical formula with structural corrections. https://arxiv.org/abs/2607.15064

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