Parity violating elastic electron scattering and neutron density distributions in the relativistic Hartree-Bogoliubov model

Parity-violating elastic electron scattering on neutron-rich nuclei is described in the framework of relativistic mean-field theory. Self-consistent ground state density distributions of Ne, Na, Ni, and Sn isotopes are calculated with the relativistic Hartree-Bogoliubov model, and the resulting neutron radii are compared with available experimental data. For the elastic scattering of 850 MeV electrons on these nuclei, the parity-violating asymmetry parameters are calculated using a relativistic optical model with inclusion of Coulomb distortion effects. The asymmetry parameters for chains of isotopes are compared, and their relation to the Fourier transforms of neutron densities is studied. It is shown that parity-violating asymmetries are sensitive not only to the formation of the neutron skin, but also to the shell effects of the neutron density distribution.