Two alternative derivations of the static contribution to the radiation-induced intermolecular energy shift

Two contrasting physical viewpoints and calculational approaches are adopted within the framework of molecular quantum electrodynamics for the evaluation of the static contribution to the change in mutual interaction energy between a pair of electric dipole polarizable molecules in an intense radiation field. This term arises when a real photon is scattered by the same molecular center with coupling between the two bodies occurring via exchange of a single virtual photon. In one method it is found that utilization of an effective three-photon interaction operator enables the energy shift to be obtained using second order perturbation theory with summation over only four time-ordered diagrams, each of which contain collapsed interaction vertices. The result is then shown to be obtained even more easily in a second approach that involves calculating the expectation values for both molecules in the ground electronic state and the field containing N photons of mode (k⃗,λ) of the electric dipole moments induced at each molecule by the incident field, which are coupled to the resonant dipole-dipole interaction tensor. The static contribution in question is shown to arise from the interaction of a permanent electric dipole moment in one species with the first hyperpolarizability of the other. Both methods are compared and contrasted with a previous computation in which contributions to the energy shift arising from 48 time-ordered diagrams were summed using fourth order perturbation theory.