Many-Body Theory of the Elastic Scattering of Electrons from Atoms and Molecules

We present a method for calculating the elastic scattering of electrons from atoms and molecules using the many-body Green's-function techniques of Martin and Schwinger. The procedure involves the self-consistent solution of a pair of equations; one for the one-particle Green's function and the other for the response function of the target in the time-dependent Hartree-Fock approximation (random-phase approximation). That both equations are one-dimensional provides a great computational advantage over more conventional techniques. We discuss the physical nature of our approximation and a numerical scheme to implement our theoretical discussion.