Multipole expansion of the retarded interatomic potential energy: derivation with the use of a dispersion relation

A dispersion relation technique is used to obtain the retarded dispersion energy of two neutral atoms in nondegenerate ground states. To that end multipole expansions are derived for the electromagnetic form factors occurring in the vertex function that characterizes the interaction of a neutral atom with a pair of photons on the mass shell. The long-range asymptotic expression for the dispersion energy is shown to contain electric and diamagnetic matrix elements in a symmetric wa