Dipole polarizability, neutron skin and symmetry energy

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 ${}^{68}$Ni, ${}^{120}$Sn, and ${}^{208}$Pb 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 ${}^{68}$Ni, ${}^{120}$Sn, and ${}^{208}$Pb are employed to predict the values of the symmetry energy parameters at saturation density and $\Delta r_{np}$. The resulting intervals are: $J=30 \text{-}35$ MeV, $L=20 \text{-} 66$ MeV; and the values for $\Delta r_{np}$ in ${}^{68}$Ni, ${}^{120}$Sn, and ${}^{208}$Pb are in the ranges: 0.15\text{-}0.19 fm,