Electromagnetic energies of nuclei and the nuclear compton amplitude

The electromagnetic energy of a nucleus is derived in perturbation theory, which relates this quantity to the amplitude for the forward scattering of virtual photons on a nucleus (nuclear Compton amplitude). Using the gauge invariance of this amplitude, the energy is separated into Coulomb and transverse components. Our formalism, although basically nonrelativistic, admits corrections of order ($\text{v}\text{c}$)² to the nuclear charge operator. The energy is further separated into one-body terms, related to the n-p mass difference, and two-body terms which lead to the Breit interaction and the nuclear Lamb shift. These results are then related to electron scattering sum rules in the manner of Cottingham. Mesonic contributions to the electromagnetic energy are also discussed.