  Neutron and proton densities of doubly-closed shell nuclei 40Ca, 48Ca and 208Pb are studied based on a Hartree-Fock model with SAMi, SAMi-J27 and SAMi-T energy density functionals (EDFs). The ground state correlations (GSC) induced by isoscalar and isovector phonons are also evaluated by the second order perturbation theory with a self-consistent random phase approximation (RPA). We found that the interior part of the ground state densities is reduced by the GSC in consistent with the experimental data. On the other hand, the GSC enhances the neutron skin thickness of 48Ca and 208Pb. The effect of GSC on the total binding energy is also evaluated by the quasi-boson approximation. The effect of the tensor interaction is found small on both the density distributions and the binding energies. 
Ground state correlations on ground state densities and total binding   energies of 40Ca, 48Ca and 208Pb