Further analysis of effective medium approximation for a tight-binding model of a liquid metal

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Abstract
Extends a previous analysis of an effective medium theory (EMA) for liquid or amorphous metals, making use of a one-orbital tight-binding model. Properties of the continuum Green function are discussed including analyticity of the solutions and the effect of non-orthogonality of the wavefunctions. It is shown that the off-diagonal part of the EMA Green function properly excludes overlap of ions, while the lack of such a property for the quasicrystalline approximation (QCA) had led to a paradox in the density of states result, which the authors resolve. Numerical results are given using exponential overlaps and several pair distribution functions, and the results are compared with the Ishida-Yonezawa theory and the QCA. The latter is found to be very unrealistic outside of the long wavelength, low energy region. An EMA calculation using the Percus-Yevick hard sphere pair distribution function gives an interesting structure in the spectral function at a finite wavevector.