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The quantum theory of an atomic beam machine is set up in matrix form. A new method is then used to derive the Bloch-Siegert shift in the resonance. The results are extended to the case of Ramsey-type excitation. Finally the Bloch-Siegert shift is computed for the present atomic beam frequency standards and found to be well below the accuracy of measurement.
J.H. Shirley (1963) studied this question.