Higher-Multipole Contributions to the Retarded van der Waals Potential

We calculate the two-photon exchange (retarded van der Waals) potential between neutral spinless systems, including the effects of higher partial waves in the atom-photon scattering amplitude. This is equivalent to including higher multipoles in the interaction of the charges in the atoms. We show that this potential can be expressed as an infinite series of terms, with coefficients that can, in principle, be measured in atom-photon scattering. The behavior of the various terms, at small separation and large separation of the system, is discussed. We show that the leading term in the contribution of each multipole has the property that it has one more power of $R^{-1\mathrm{}}$ in its large-$R$ behavior than in its small-$R$ behavior.