Nuclear charge radii: Density functional theory meets Bayesian neural networks

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.

14 pages, 6 figures

References in corpus (8)

• Neutron-Rich Nuclei in Heaven and Earth
• Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XII: Stiffness and stability of neutron-star matter
• Building relativistic mean field models for finite nuclei and neutron stars
• Evolution of shell structure in neutron-rich calcium isotopes
• An artificial neural network application on nuclear charge radii
• Decoding Beta-Decay Systematics: A Global Statistical Model for Beta^- Halflives
• New charge radius relations for atomic nuclei
• Application Of Support Vector Machines To Global Prediction Of Nuclear Properties

Cited by in corpus (3)

• Nuclear mass predictions based on Bayesian neural network approach with pairing and shell effects
• Validating neural-network refinements of nuclear mass models
• Emergence of low-energy monopole strength in the neutron-rich calcium isotopes