The Semi-Classical Theory of Radiation and the Einstein Coefficients

George William Series

R. Bullough, P. J. Caudrey, A.‐S. F. Obada

A natural all-order decorrelation procedure is described for the interaction of a single two-level atom with all modes of the radiation field which replaces the semi-classical boson approximation for the atom by an exact fermion treatment. In consequence the vacuum Lamb shift appears as twice the Bethe shift for each level separately instead of the limiting neo-classical shift obtained in the Bose theory. Stimulated emission and absorption modify the Einstein A-coefficient and the vacuum shift is extended to include a field dependent shift. The all-order decorrelated perturbation theory yields an equation of motion for the single-atom dipole moment which includes those reported from operator radiation reaction theory recently; but it also generalizes these by including the effects of stimulated processes. The method is extended to a many-atom case in which it becomes necessary to modify the procedure slightly.

Wolfgang Ernst Friederich Pauli

Alan Corney

Starting from the absorption of radiation by a classical electron oscillator, Einstein's A and B coefficients for spontaneous and stimulated transitions are introduced. Stimulated transition rates are derived by time-dependent perturbation theory. Relations between the Einstein B coefficients and oscillator strengths are also determined. The atomic frequency response for stimulated transitions is explained.

Miguel Orszag

Steven Weinberg