Investigation of the difference in charge radii of mirror pairs with deep Bayesian neural networks
X. Zhang, H. He, Guofeng Qu, X. Liu, H. Zheng, W. Lin, Jungong Han, P. Ren, R. Wada
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.