Averaging the resolvent with a space-correlated random potential

The problem of the quasi-particle spectrum in a binary disordered alloy with a space-orrelated random potential is considered. The extended space formalism is used to represent the average resolvent. To calculate the mass operator, some self-consistent approximation procedures are suggested that coincide with the well-known self-consistent approximations for $\alpha =0$ (where $\alpha$ is the short-range order parameter). The elaborated theory ensures the correct passage to the Green's function of a perfect crystal in the limits $\alpha\to 1$ and $\alpha\to -1$ for any concentration and 50 approximations possess the correct analytic properties for all values of the parameter $\alpha$.