Quantum Theory of X-Ray Diffraction by a Crystal

A new formulation of the theory of X-ray diffraction by a crystal using techniques of quantum field theory has been developed. The classical field amplitudes of previous theories are replaced, in the present work, by scattering amplitudes for the transmitted and diffracted beams which are obtained from a photon Green's function. The case of a single-Bragg reflection for a parallel sided crystal has been treated in detail. The scattering amplitudes for this case give results which are essentially those of the semi-classical dynamical theory with absorption. The application of the theory to the diffraction of a beam of finite width for the Laue geometry provides an alternate demonstration that the beam emerges from the exit surface of the crystal at a point given by the direction of energy flow.