Exact Solution of the One-Particle Model of Exchange Scattering in Solids

Abstract

A solution of the Chew-Low equations describing exchange scattering of conduction electrons is presented, which is exact within the one-particle intermediate-state approximation. This solution shares with earlier, approximate ones the feature that for antiferromagnetic exchange the spin-flip scattering amplitude can develop complex poles on the physical sheet. To examine this point further, the theory is generalized to an interaction of finite range, analyticity in momentum transfer being assumed and spin-orbit coupling being neglected. This still does not guarantee removal of the complex poles. However, the forward-scattering amplitude appears to be free from poles in all these cases. Unitarity is satisfied in the appropriate zero-temperature limit.