The neutron skin thickness from the measured electric dipole polarizability in 68Ni, 120Sn, and 208Pb

The information on the symmetry energy and its density dependence is deduced by comparing the available data on the electric dipole polarizability alpha(D) of Ni-68, Sn-120, and Pb-208 with the predictions of the random-phase approximation, using a representative set of nuclear energy density functionals. The calculated values of alpha(D) are used to validate different correlations involving alpha(D), the symmetry energy at the saturation density J, the corresponding slope parameter L, and the neutron skin thickness Delta r(np), as suggested by the droplet model. A subset of models that reproduce simultaneously the measured polarizabilities in Ni-68, Sn-120, and Pb-208 are employed to predict the values of the symmetry energy parameters at saturation density and Delta r(np). The resulting intervals are J = 30-35 MeV, L= 20-66 MeV; and the values for Delta r(np) in Ni-68, Sn-120, and Pb-208 are in the ranges 0.15-0.19, 0.12-0.16, and 0.13-0.19 fm, respectively. The strong correlation between the electric dipole polarizabilities of two nuclei is instrumental to predict the values of electric dipole polarizabilities in other nuclei.