We study whether the neutron skin thickness $\Delta r_{ np}$ of ${ }^{ 208}$Pb originates from the bulk or from the surface of the neutron and proton density distributions in mean field models. We find that the size of the bulk contribution to $\Delta r_{ np}$ of ${ }^{ 208}$Pb strongly depends on the slope of the nuclear symmetry energy, while the surface contribution does not. We note that most mean field models predict a neutron density for ${ }^{ 208}$Pb between the halo and skin type limits. We investigate the dependence of parity- violating electron scattering at the kinematics of the PREX experiment on the shape of the nucleon densities predicted by the mean field models for ${ }^{ 208}$Pb. We find an approximate formula for the parity-violating asymmetry in terms of the central radius and the surface diffuseness of the nucleon densities of ${ }^{ 208}$Pb in these models.
Categories: nucl-th nucl-ex