Nuclear charge radii in Bayesian neural networks revisited

TL;DR

This paper introduces a refined Bayesian neural network model that accurately predicts nuclear charge radii across a range of isotopes, demonstrating high precision and reliability in extrapolation scenarios.

Contribution

The work presents a novel BNN approach with engineered features to improve the prediction of nuclear charge radii, especially for exotic isotopes.

Findings

RMS deviation of 0.014 fm for charge radii predictions

Accurate predictions for proton-rich and neutron-rich calcium isotopes

Reliable extrapolation performance across different nuclear properties

Abstract

In this work, a refined Bayesian neural network (BNN) based approach with six inputs including the proton number, mass number, and engineered features associated with the pairing effect, shell effect, isospin effect, and ``abnormal" shape staggering effect of $^{181,183,185}$Hg, is proposed to accurately describe nuclear charge radii. The new approach is able to well describe the charge radii of atomic nuclei with $A\ge40$ and $Z\ge20$. The standard root-mean-square (rms) deviation is $0.014$ fm for both the training and validation data. In particular, the predicted charge radii of proton-rich and neutron-rich calcium isotopes are found in good agreement with data. We further demonstrate the reliability of the BNN approach by investigating the variations of the rms deviation with extrapolation distances, mass numbers, and isospin asymmetries.