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, which only get reinforced by recent experimental measurements. In this letter, 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 ≥ 40 and Z ≥ 20 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.

Local variations of charge radii for nuclei with even $Z$ from 84 to 120

“…Although these algebraic expressions provide a simple method for estimating nuclear charge radii, the fine details of nuclear structure cannot be covered well. However, as a prior constraint relation, a available formula is necessary in the simulations of machine learning process [41,50].…”

“…However, the difficulty was encountered in heavy or superheavy regions due to the limitation of computing power. Recently developed Bayesian neural networks (BNNs) are devoted to accurate predictions of nuclear charge radii [40,41].…”