Frequency Shift in High-Intensity Compton Scattering

The frequency shift predicted by Brown and Kibble, and by Goldman, for a photon scattered out of an intense beam by a free electron is re-examined. It is shown that the effect has a very simple classical interpretation, as a Doppler shift arising from the nonzero average velocity of the electron in the beam. The discrepancy between this prediction and the recent perturbation calculation of Fried and Eberly is shown to arise from the use, in the latter, of a pure monochromatic beam rather than a wave train of finite length. It is shown that the effect should arise for a quantized photon beam as well as for a classical one. The question of energy-momentum conservation is discussed. With the help of a one-dimensional model which exhibits all the essential features of the effect, it is shown that the extra energy and momentum which are generated in the scattering process are taken up by the beam itself in the form of an extremely small shift in the average momentum of a photon in the beam. The possibility of experimental detection of the effect is briefly discussed.