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The coherent excitation of several atomic states by inelastic electron scattering and their subsequent radiative decay is considered. General expressions are derived for the photon counting rate in a quantum-beat experiment, and for the total number of photons counted in a level-crossing experiment. The general results are used to calculate the phase of the oscillatory part of the photon counting rate in the Hadeishi-Nierenberg quantum-beat experiment.
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Robert L. Kelly (1966) studied this question.
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