Forward-Scattering Approximation for Disordered Systems

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Abstract
Changes in the Fermi surface with disorder can be defined for only two cases: (a) when ordinary perturbation theory is applicable and (b) when the forward-scattering approximation is applicable. In the forward-scattering approximation (FSA) the perturbation is large in the vicinity of the forward direction or diagonal elements, but the average off-diagonal element is small, in contrast to the ordinary perturbation approximation where all perturbing matrix elements are small. The multiple scattering problem is solved for the FSA, and its close relation to ordinary perturbation theory is discussed. All the results of ordinary perturbation theory can be carried over to the FSA if proper account is taken of the self-energies of the states and interband mixing. The self-consistent condition on the potential imposed by shielding is given. The fact that the FSA can satisfy this self-consistency makes it a physically realistic approximation. All systems with a large concentration of disorder whose properties still can be approximated by the concepts of ordered systems, such as a Fermi surface, must be describable by either the FSA or ordinary perturbation theory.