Investigation of the difference in charge radii of mirror pairs with deep Bayesian neural networks

Abstract

The relationship of the root-mean-square (rms) charge radius difference $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{ch}}^{\mathrm{mir}}$ of mirror pairs and the isospin asymmetry $(N\ensuremath{-}Z)/A$ is investigated using a newly developed deep Bayesian neural network (DBNN) approach. The DBNN approach with optimized architecture and input features demonstrates superior predictive capability for nuclear rms charge radii ${R}_{\mathrm{ch}}$ compared to previous machine learning approaches employing single-layer neural networks. Utilizing the DBNN-predicted ${R}_{\mathrm{ch}}$ values, a significant mass dependence of the $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{ch}}^{\mathrm{mir}}$ versus $(N\ensuremath{-}Z)/A$ linear relationship, previously unobserved in experimental $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{ch}}^{\mathrm{mir}}$ analyses, is revealed. The physical existence and origin of the mass-dependent linear relationship between $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{ch}}^{\mathrm{mir}}$ and $(N\ensuremath{-}Z)/A$ is explored using the microscopic Sky3D model and the macroscopic droplet model. Both Sky3D model and droplet model calculations indicate the physical existence of a mass-dependent linear relationship between $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{ch}}^{\mathrm{mir}}$ and $(N\ensuremath{-}Z)/A$ in nature. Within the droplet model framework, the mass dependence is found to be closely associated with the ratio of the volume and surface symmetry energy coefficients, suggesting that such a mass-dependent $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{ch}}^{\mathrm{mir}}$ versus $(N\ensuremath{-}Z)/A$ linear relationship could potentially serve as a probe for studying the surface component in nuclear symmetry energy in future.