Abstract
The momentum-translation approximation is valid for electromagnetic transitions in bound systems caused by external radiation of photon energy much less than the transition energy. Its utility is explored here for two types of problems that violate that restriction. One application is to resonant bound-bound multiphoton transitions of low multiphoton order, and results are compared to recent perturbative calculations. The other application is to both the transition rate and the spectrum of two-photon spontaneous emission from the metastable $2S$ state in hydrogen. Predicted transition rates are too low, but the spectrum agrees well with the known results. All momentum-translation results follow from simple closed-form analytical expressions.
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