Electronic states in liquid and amorphous metals. II. New approach to the average spectrum

We present a method for evaluating the spectral function $A(k,E)\mathrm{}$ in a structurally disordered system directly, rather than as a by-product of an approximate calculation of the average Green's function. Our method is based, in part, on Roth's effective-medium approximation but is so formulated as to guarantee $A(k,E)>0\mathrm{}$ independent of the strength of the atomic scattering. The general structure of the new equations is shown to be analogous to that of the corresponding coherent-potential equations for the alloy problem.