Sensitivity of the electric dipole polarizability to the neutron skin thickness in ${}^{208}$Pb

The static dipole polarizability, ${\alpha }_{\mathrm{D}}$, in ${}^{208}$Pb has been recently measured with high-resolution via proton inelastic scattering at the Research Center for Nuclear Physics (RCNP). This observable is thought to be intimately connected with the neutron skin thickness, $r_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}$, of the same nucleus and, more fundamentally, it is believed to be associated with the density dependence of the nuclear symmetry energy. The impact of $r_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}$ on ${\alpha }_{\mathrm{D}}$ in ${}^{208}$Pb is investigated and discussed on the basis of a large and representative set of relativistic and non-relativistic nuclear energy density functionals (EDF).