  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.
