Polarizability effects in electronic and muonic atoms

TheS state polarizability shifts are derived from the virtual forward Compton scattering in the unretarded dipole approximation. In the non-relativistic limit ωN/2m≪1, the shift is proportional to the photonuclear sum rule σ−3/2, while in the relativistic limit ωN/2m≫1 it is proportional to a logarithmically weighted σ−2 sum rule. In both cases, the characteristic momentum transfer is (2mωN)1/2. The non-locality from the intermediate lepton propagation removes the divergence typical of the static limit. Explicit formulas for the shifts are given for both the relativistic and non-relativistic limits