Multiple-Time-Scale Perturbation Theory and Constant Atomic Transition Rates

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Abstract
A conventional perturbation approach to the problem of induced emission by an atom exposed to electromagnetic radiation is reviewed. The calculation is known to contain a familiar mathematical anomaly requiring a nonphysical restraint on the time range of validity of the derived expression for the atomic transition rate. The problem is then solved again in the formalism of multiple-time-scale perturbation theory. This approach avoids the mathematical difficulty in question, and yields for the transition rate a more general expression. During the restricted time interval, in which the conventionally obtained result is valid, it and the more general expression are identical.