On the configurational average of the Green's function for liquid metals

Abstract

Ballentine and Heine (1964) have analysed the theory of Phariseau and Ziman (1963) relating to the theory of liquid metals with the view of finding the precise mathematical approximation. They pointed out that previous investigators averaged the inverse of the Green's function over possible configurations instead of averaging it directly. In this note the direct averaging of the Green's function is discussed and it is shown that the degree of approximation of the P-Z formula is higher than they had expected. This means that if one averages each term of the infinite series for the Green's function by introducing the same approximation as P-Z used when they averaged the reciprocal of the Green's function and then sums the series, one obtains the same Green's function as the one which P-Z obtained.