  We analyze the neutron skin thickness in finite nuclei with the droplet model
and effective nuclear interactions. The ratio of the bulk symmetry energy J to
the so-called surface stiffness coefficient Q has in the droplet model a
prominent role in driving the size of neutron skins. We present a correlation
between the density derivative of the nuclear symmetry energy at saturation and
the J/Q ratio. We emphasize the role of the surface widths of the neutron and
proton density profiles in the calculation of the neutron skin thickness when
one uses realistic mean-field effective interactions. Next, taking as
experimental baseline the neutron skin sizes measured in 26 antiprotonic atoms
along the mass table, we explore constraints arising from neutron skins on the
value of the J/Q ratio. The results favor a relatively soft symmetry energy at
subsaturation densities. Our predictions are compared with the recent
constraints derived from other experimental observables. Though the various
extractions predict different ranges of values, one finds a narrow window L ~
45-75 MeV for the coefficient L that characterizes the density derivative of
the symmetry energy which is compatible with all the different empirical
indications.
