  We study whether the neutron skin thickness (NST) of 208Pb 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 NST 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 relativistic models, predict a
bulk contribution in NST of 208Pb about twice as large as the surface
contribution. In contrast, models with a soft symmetry energy like common
nonrelativistic models predict that NST of 208Pb 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 NST of
208Pb with the density derivative of the nuclear symmetry energy arises from
the bulk part of NST. We also note that most models predict a mixed-type
(between halo and skin) neutron distribution for 208Pb. 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 208Pb 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 208Pb
nucleon densities.
