Theoretical study on nuclear structure by the multiple Coulomb scattering and magnetic scattering of relativistic electrons

Electron scattering is an effective method to study the nuclear structure. For the odd-$A$ nuclei with proton holes in the outmost orbits, we investigate the contributions of proton holes to the nuclear quadrupole moments $Q$ and magnetic moments $\mu$ by the multiple Coulomb scattering and magnetic scattering. The deformed nuclear charge densities are constructed by the relativistic mean-field (RMF) models. Comparing the theoretical Coulomb and magnetic form factors with the experimental data, the nuclear quadrupole moments $Q$ and nuclear magnetic moments $\mu$ are investigated. From the electron scattering, the wave functions of the proton holes of odd-$A$ nuclei can be tested, which can also reflect the validity of the nuclear structure model.