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

2026/07/16 by Pengfei Ma, Minghui Hu, Kai Ren +2
#nucl-th

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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 (BECR₁p) 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.

Citations

• Self-consistent mean-field models for nuclear structure

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