Nuclear charge radii: Density functional theory meets Bayesian neural networks

TL;DR

This paper combines density functional theory with Bayesian neural networks to significantly improve predictions of nuclear charge radii and provide theoretical error estimates, enhancing nuclear structure modeling accuracy.

Contribution

It introduces a novel hybrid approach that refines nuclear charge radius predictions using Bayesian neural networks trained on residuals from density functional theory.

Findings

BNN refinement improves prediction accuracy by over 40%

The approach provides theoretical error bars for predictions

Significant enhancement over traditional density functional theory results

Abstract

The distribution of electric charge in atomic nuclei is fundamental to our understanding of the complex nuclear dynamics and a quintessential observable to validate nuclear structure models. We explore a novel approach that combines sophisticated models of nuclear structure with Bayesian neural networks (BNN) to generate predictions for the charge radii of thousands of nuclei throughout the nuclear chart. A class of relativistic energy density functionals is used to provide robust predictions for nuclear charge radii. In turn, these predictions are refined through Bayesian learning for a neural network that is trained using residuals between theoretical predictions and the experimental data. Although predictions obtained with density functional theory provide a fairly good description of experiment, our results show significant improvement (better than 40%) after BNN refinement. Moreover, these improved results for nuclear charge radii are supplemented with theoretical error bars. We have successfully demonstrated the ability of the BNN approach to significantly increase the accuracy of nuclear models in the predictions of nuclear charge radii. However, as many before us, we failed to uncover the underlying physics behind the intriguing behavior of charge radii along the calcium isotopic chain.