Relativistic eikonal approaches to parity violating electron-nucleus scattering

Abstract

The Coulomb electron scattering on even-even nuclei and the magnetic electron scattering on odd-$A$ nuclei have been investigated in the relativistic eikonal approximation and in the plane wave Born approximation, respectively. In this article, we generalize the relativistic eikonal approximation to the parity violating electron scattering on even-even nuclei. The parity violating asymmetries at electron energy of 850 MeV are calculated for three typical cases: Ca isotopes, $N=50$ isotones, and $N=Z$ doubly magic nuclei. In calculations the proton and neutron densities are obtained from the relativistic mean-field theory. The parity violating asymmetries are analyzed by comparing both the form factors and the densities of neutrons and protons. It is found that the parity violating asymmetries are sensitive to the differences between neutron and proton densities. Our results provide useful references for the parity violating electron-nucleus scattering experiments in the future.