Extracting neutron skin from elastic proton-nucleus scattering with deep neural network

Based on the relativistic impulse approximation of proton-nucleus elastic scattering theory, the nucleon density distribution and neutron skin thickness of ${}^{48}$Ca are estimated via the deep learning method. The neural-network-generated densities are mainly compressed to be lower inside the nucleus compared with the results from the relativistic PC-PK1 density functional, resulting in a significant improvement on the large-angle scattering observables, both for the differential cross section and analyzing power. The neutron skin thickness of ${}^{48}$Ca is captured to be 0.211(11) fm. The relatively thicker neutron skin is deemed reasonable from the perspective of density functional analysis.