Origin of the neutron skin thickness of Pb-208 in nuclear mean-field models

We study whether the neutron skin thickness Delta r(np) of Pb-208 originates from the bulk or from the surface of the nucleon density distributions, according to the mean-field models of nuclear structure, and find that it depends on the stiffness of the nuclear symmetry energy. The bulk contribution to Delta r(np) arises from an extended sharp radius of neutrons, whereas the surface contribution arises from different widths of the neutron and proton surfaces. Nuclear models where the symmetry energy is stiff, as typical of relativistic models, predict a bulk contribution in Delta r(np) of Pb-208 about twice as large as the surface contribution. In contrast, models with a soft symmetry energy like common nonrelativistic models predict that Delta r(np) of Pb-208 is divided similarly into bulk and surface parts. Indeed, if the symmetry energy is supersoft, the surface contribution becomes dominant. We note that the linear correlation of Delta r(np) of Pb-208 with the density derivative of the nuclear symmetry energy arises from the bulk part of Delta r(np). We also note that most models predict a mixed-type (between halo and skin) neutron distribution for Pb-208. Although the halo-type limit is actually found in the models with a supersoft symmetry energy, the skin-type limit is not supported by any mean-field model. Finally, we compute parity-violating electron scattering in the conditions of the Pb-208 parity radius experiment (PREX) and obtain a pocket formula for the parity-violating asymmetry in terms of the parameters that characterize the shape of the Pb-208 nucleon densities