Abstract
A method, alternate to that of conventional perturbation theory, is developed and illustrated for the computation of the photoionization of atoms by photons with energies less than the atomic ionization potential. The method allows treatment of the electromagnetic field to all orders at a rather simple level of analysis. It represents, in fact, a slight generalization of the Born approach to the theory of scattering. As a consequence of certain approximations, simple analytic formulae are obtained to describe multiple photon ionization events. Because of one of the approximations (a situation straightforwardly rectifiable, but not attempted here for the sake of illustrative simplicity), the formulae obtained here are probably only qualitatively interesting.
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