Muffin-tin model of a liquid metal: Electronic density of states in a modified quasicrystalline approximation

In the muffin-tin model of a liquid metal, the individual scattering centers are represented by nonoverlapping, spherically symmetric atomic potentials. Given a specific configuration of the scatterers, it can be shown that the atomic potentials enter the calculation of the density of states $\rho \mathrm{}\left(E\right)\mathrm{}$ only through the atomic phase shifts ${\delta }_l\mathrm{}\left(E\right)\mathrm{}$. The quantities of physical interest, however, are given by an average over all possible configurations and are usually evaluated in terms of a single site decoupling of the multiple-scattering series. Once such an approximation is made, it is no longer clear that the mean density of states $〈\rho \mathrm{}\left(E\right)\mathrm{}〉$ can be expressed in terms of just the quantities ${\delta }_l\mathrm{}\left(E\right)\mathrm{}$. [Physically, the decoupling may introduce a spurious overlap of the potentials and the evaluation of $〈\rho \mathrm{}\left(E\right)\mathrm{}〉$ would then require the off-shell matrix elements of the atomic-scattering operators.] In particular, the familiar quasicrystalline approximation (QCA) is shown to exhibit this deficiency. We suggest a modified QCA which overcomes this deficiency by providing a more realistic description of the atomic correlations. The applicability of our method is illustrated by calculations based on a one-dimensional model. We also discuss the qualitative behavior of the quasiparticle spectrum of a realistic three-dimensional transition- or noble-metal liquid.