Extracting nuclear charge radii from binding energies: a single-parameter empirical formula with structural corrections
arXiv:2607.15064
The paper introduces a one‑parameter empirical formula that links nuclear binding energies to charge radii, adding shell, odd‑even, finite‑size, and deformation corrections to achieve high accuracy, and further refines predictions with anisotropic kernel ridge regression.
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 () 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.
15 pages, 5 figures, 1 table