Extension of the single-atom approximation with allowance for short- and long-range order in alloys

A method is proposed for finding the corrections to the coherent potential approximation based on exact summation of all contributions to the Green's function of an alloy due to scattering by different pairs of atoms. The expressions are obtained with allowance for short- and long-range order in the alloys. Estimates are made of the corrections to the obtained expressions for the configuration averaged $T$ scattering matrix and the density of electron states due to scattering by groups of three or more atoms. It is shown that in many important cases the obtained expressions are valid for alloys with arbitrary impurity concentrations. The density of electron states is calculated for binary alloys with bcc lattice for different values of the parameters of the short- and long-range order.