An expression for the integrated density of states of a liquid metal in Roth's effective-medium approximation. A generalisation of Friedel's formula

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Abstract
An expression for the integrated density of states of a liquid metal is given in Roth's effective-medium approximation. The expression can be regarded as a generalisation of the Friedel formula for the single-impurity problem to the situation where an infinite number of scattering potentials are distributed irregularly with finite density throughout all space. It is applicable to both the tight-binding- and the muffin-tin-potential models of liquid metals and is useful for accurate determination of the Fermi levels for these model liquid metals. It is also useful for showing that the EMA preserves several sum rules for the density of states.