Center-of-mass projection Skyrme-Hartree-Fock densities

We investigate the effects of center-of-mass projection on the nuclear charge density resulting from self-consistent calculations using the effective Skyrme interaction. We compare the full projection with the widely used standard recipe which corrects for the spurious center-of-mass motion by unfolding a harmonic oscillation. We find that full projection is necessary for a quantitative description in light nuclei at least up to the Ca isotopes. The variations of the effect with varying Skyrme forces are studied. A microscopic derivation of the standard recipe, the oscillator correction, is given. (orig.)