The coherent-potential approximation (CPA) for both single-particle and two-particle Green's functions are rederived using locator expansion method proposed by Matsubara and Toyozawa. Instead of using self-contained cumulant expansion to treat the excluded volume effects for atoms, we use a diagrammatic method with the idea first proposed by Yonezawa. A systemmatic method is used to generate self-consistent equations for all single-site diagrams. We emphasis our treatment for two-particle Green's function which can be extended to obtain the corresponding CPA equation for electrical conductivity in liquid metals and amorphous solids.
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