Multiple-Scattering Methods in the Theory of Solids

The formalism of solid-state scattering theory is applied to the construction of the t matrix for a pair of electrons interacting through a repulsive potential of finite range. Expressions for t are obtained in suitable limits for three cases: (1) a potential acting only at a single site and in a single band, (2) a potential acting at a single site but connecting a pair of bands, and (3) a potential acting in a single band but extending to first neighbors. The results are applied to the determination of an optical potential which can be used in a study of the range of excited electrons in metals, and to the determination of the ground-state energy of a low-density system. The ground-state energy is examined as a function of spin alignment, leading to the development of criteria for the occurrence of ferromagnetism in the low-density limit. It is shown that for repulsive, finite-range interactions, ferromagnetism does not occur for very low densities, whatever the band structure is.