Novel Bayesian neural network based approach for nuclear charge radii

Abstract

Charge radius is one of the most fundamental properties of a nucleus. However, a precise description of the evolution of charge radii along an isotopic chain is highly nontrivial, as reinforced by recent experimental measurements. In this paper, we propose a novel approach which combines a three-parameter formula and a Bayesian neural network. We find that the novel approach can describe the charge radii of all $A\ge40$ and $Z\ge20$ nuclei with a root-mean-square deviation about 0.015 fm. In particular, the charge radii of the calcium isotopic chain are reproduced very well, including the parabolic behavior and strong odd-even staggerings. We further test the approach for the potassium isotopes and show that it can describe well the experimental data within uncertainties.