Optical theorem and multiple-scattering theory. Electronic states in substitutional alloys

When multiple-scattering theory is used to describe the electronic properties of disordered transition-metal systems, decoupling procedures which appear to be physically reasonable can lead to negative densities of states in the vicinity of the resonant $d$ bands. We present a method, based on the application of the optical theorem to the total scattering operator, that allows us to determine a priori which approximation schemes can be relied upon to produce a positive spectrum. The application of this method to substitutionally disordered binary alloys is discussed here. We find that both the average-$t$-matrix and coherent-potential approximations will always yield nonnegative densities of states. The application of our technique to approximations based on the Lloyd formula for the density of states is also discussed.