Effective-medium theory of electronic states in structurally disordered metals: Application to liquid Cu

We consider the application of the effective-medium approximation (EMA) to the muffin-tin model of a liquid metal. The spherical symmetry of the average liquid is used to reduce the momentum ($\overrightarrow{\mathrm{k}}$)-dependent self-consistency requirements of the theory to a form in which they involve one-dimensional rather than three-dimensional integrations. We also show that, within the EMA, a closed expression for the integrated density of states can be derived, and that this expression provides a useful check on the convergence of the self-consistent equations. The theory is applied to liquid Cu. The self-consistent equations converge without difficulty and the resulting electronic spectrum is in substantial agreement with recent photoemission data. Our results are compared with an alternate approach to the muffin-tin EMA suggested by Asano and Yonezawa. The two approaches yield similar densities of states but markedly different behavior for the special functions.