Nonrelativistic Compton scattering in Furry’s picture: Beyond the sudden impulse approximation by means of the complex coordinate method

Basic electrodynamical and collision theory presumptions related to Compton scattering are critically reconsidered (with particular emphasis on identifying the proper transition matrix element effectively controlling the process, and on framing it within time dependent perturbation theory and scattering theory) in order to indicate the main features and the validity of the proposed method. The on-energy-shell transition matrix element governing the cross-sectional formula is obtained from Furry’s two-potential formalism, which makes possible a treatment of the primary electron–photon interaction to first order while incorporating the effects of the final state Coulombic interaction to all orders. Furry’s procedure, in addition to defining clearly which initial and final states should enter the transition matrix element, also brings additional insight into the nature of the so-called ‘‘sudden impulse approximation.’’ A treatment is proposed in which the decisive transition matrix element is obtained without explicit calculation of the distorted continuum solutions implied by Furry’s procedure, but is instead extracted from the dispersion relations of the ‘‘beat-frequency’’ dependent generalized polarizability by means of the L2 treatment based on the complex-coordinate method. The practical advantage of the method will be its ability to incorporate correlation between the ejected electron and the electrons remaining in the ion.