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

The relationship of the root-mean-square (rms) charge radius difference ΔRchᵐⁱʳ of mirror pairs and the isospin asymmetry (N-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 Rch compared to previous machine learning approaches employing single-layer neural networks. Utilizing the DBNN-predicted Rch values, a significant mass dependence of the ΔRchᵐⁱʳ versus (N-Z)/A linear relationship, previously unobserved in experimental ΔRchᵐⁱʳ analyses, is revealed. The physical existence and origin of the mass-dependent linear relationship between ΔRchᵐⁱʳ and (N-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 ΔRchᵐⁱʳ and (N-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 ΔRchᵐⁱʳ versus (N-Z)/A linear relationship could potentially serve as a probe for studying the surface component in nuclear symmetry energy in future.