Coherent potential method in the theory of disordered alloys

Green's function of disordered alloy averaged over all configurations is written down in the form of infinite series, in which every next term includes one extra summation over the intermediate momenta. The first and second terms of the series correspond to the coherent potential approximation. It is shown that for the one band model the small parameter of the theory is $(a/R_0)^3$, where $a$ is the lattice constant, $R_0$ – the length of the electron hopping over the lattice. For the two bands $sd$-model the small parameter is $\gamma/W$, where $\gamma$ is the constant of $sd$-hybridization, $W$ – the width of the $s$-band. It is shown that the series for the Green function is convergent for all values of energy except those close to the edges of the bands. The effect of the shortest range order in the alloy on the energy spectrum, is estimated.