Method of $\gamma$ expansions in the electronic theory of disordered alloys

In the electronic theory of disordered alloys an expansion with respect to the parameter $\gamma=\exp(-1/\xi)$, where $\xi$ is the dimensionless correlation length of the single-electron Green's function, is proposed. This expansion makes it possible to take into account the presence in the alloy of short-range order and the effects of multiple scattering of the electrons by different sites. It is shown that in the case of sufficiently strong disorder $\gamma$ is a small parameter of the coherent potential approximation, and the corrections to this approximation are found. It is also shown that in the framework of this approximation the equilibrium values of the parameters of the short-range order can be calculated.