  The density dependence of the symmetry energy around saturation density,
characterized by the slope parameter L, is studied using information provided
by the neutron skin thickness in finite nuclei. An estimate for L is obtained
from experimental data on neutron skins extracted from antiprotonic atoms. We
also discuss the ability of parity-violating elastic electron scattering to
obtain information on the neutron skin thickness in 208Pb and to constrain the
density dependence of the nuclear symmetry energy. The size and shape of the
neutron density distribution of 208Pb predicted by mean-field models is briefly
addressed. We conclude with a comparative overview of the L values predicted by
several existing determinations.
