Radiative Effects in Semiclassical Theory

Unquantized field calculations are extended to include the effect of an atom's field acting back upon the atom. It is shown that, in the absence of an applied field, semiclassical theory predicts that an atom will decay spontaneously from an excited state with a characteristic time equal to the reciprocal of the Einstein $A$ coefficient for the transition. The theory also predicts that the frequency of the light radiated during a transition will have a small time dependence. The corresponding frequency shifts are compared with the Lamb shift in hydrogen. The derived equations are used to study the response of a many-level atom to an applied, monochromatic field. In the case of a three-level system, it is predicted that optical nutations are not just limited to the resonant transition, but are also present in the fluorescence involving the other level.