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Nonrelativistic atom-photon interaction beyond the multipole approximation

We investigate the interaction between the hydrogen atomic orbitals and the quantized modes of the electromagnetic field within the domain of nonrelativistic quantum electrodynamics in the Coulomb gauge. Contrary to the conventional dipole approximation and higher-order multipole approximations, which hold in the long-wavelength regime, we make no such approximations and investigate the rigorous wavelength dependence of the interaction matrix elements. Using analytical as well as numerical considerations, we establish the short-wavelength behaviour in the domain that is beyond the multipole approximation but still within the nonrelativistic regime. Our results differ significantly from the predictions of the dipole approximation. These features are graphically demonstrated in the case of the radiative 1s-2pz coupling in the hydrogen atom. We report a previously unnoticed short-wavelength contribution to the interaction that vanishes in the multipole expansion. We note that the convergence properties of radiative energy shifts are incorrectly predicted by the dipole approximation and that the unapproximated result is in fact quickly convergent.