Electric dipole polarizability constraints on neutron skin and symmetry energy

We review the experimental knowledge on the dipole polarizability (DP) of nuclei and its relation to the neutron skin thickness and properties of the neutron-rich matter equation of state (EOS). The discussion focuses on recent experiments using relativistic Coulomb excitation in inelastic proton scattering at extreme forward angles covering a mass range from $^{40}$Ca to $^{208}$Pb. Constraints on the neutron skins and the density dependence of the symmetry energy are derived from systematic comparison to calculations based on density functional theory (DFT) and ab initio methods utilizing interactions derived from chiral effective field theory ($\chi$EFT). The results consistently favor a soft EOS around or slightly below the saturation point. An outlook is given on possible improvements of the precision achievable in stable nuclei and studies of exotic neutron-rich unstable nuclei with upcoming experimental facilities.