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We analyze the neutron skin thickness in finite nuclei with the droplet modeland effective nuclear interactions. The ratio of the bulk symmetry energy J tothe so-called surface stiffness coefficient Q has in the droplet model aprominent role in driving the size of neutron skins. We present a correlationbetween the density derivative of the nuclear symmetry energy at saturation andthe J/Q ratio. We emphasize the role of the surface widths of the neutron andproton density profiles in the calculation of the neutron skin thickness whenone uses realistic mean-field effective interactions. Next, taking asexperimental baseline the neutron skin sizes measured in 26 antiprotonic atomsalong the mass table, we explore constraints arising from neutron skins on thevalue of the J/Q ratio. The results favor a relatively soft symmetry energy atsubsaturation densities. Our predictions are compared with the recentconstraints derived from other experimental observables. Though the variousextractions predict different ranges of values, one finds a narrow window L ~45-75 MeV for the coefficient L that characterizes the density derivative ofthe symmetry energy which is compatible with all the different empiricalindications.

Neutron skin thickness in droplet model with surface width dependence: indications of softness of the nuclear symmetry energy