Long-Range Retarded Potentials between Molecules

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Abstract
The retarded interaction between neutral systems with no permanent moments, i.e., relativistic dispersion forces, is analyzed by quantum electrodynamics and the two‐photon exchange potential is computed for three cases: (i) When both systems are in their ground states, where the potential is the Casimir—Polder potential which falls off for separations R greater than λ/, the characteristic reduced wavelength in dipole transitions, as R−7; (ii) when one system is in an optically allowed excited state where the potential at short distances is the well‐known resonance potential proportional to R−3; and (iii) when both molecules are in excited states. The interaction energies are computed at all separations larger than a few molecular radii, so all overlap and Pauli effects are not considered. The asymptotic forms are given both for R>λ/ and R<λ/ (but still larger than molecular size). The latter give the familiar London and resonance potentials. The former are new results and show a very much slower falloff like a modulated inverse distance or distance squared. This effect is due to the true radiation field of a dipole containing in the radiation zone fields which fall off as R−1. The London potentials, calculated normally by Coulomb interaction only, arise in the fully retarded theory from the near‐zone fields which fall off as R−3.

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