Novel Bayesian neural network based approach for nuclear charge radii

TL;DR

This paper introduces a new method combining a three-parameter formula with Bayesian neural networks to accurately predict nuclear charge radii across various isotopic chains, achieving high precision and capturing complex behaviors.

Contribution

The paper presents a novel hybrid approach that improves the modeling of nuclear charge radii, especially for calcium and potassium isotopes, with high accuracy and uncertainty quantification.

Findings

Achieves RMS deviation of 0.015 fm for nuclei with A≥40, Z≥20.

Successfully reproduces charge radii and odd-even staggering in calcium isotopes.

Accurately describes experimental data for potassium isotopes within uncertainties.

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.