DEFINITION OF EXCHANGE BASED ON CUMULANT EXPANSION - CORRELATION INDUCED NARROWING OF THE EXCHANGE HOLE

Under the assumption, that the cumulant expansion of the reduced density matrices has a fundamental meaning, a corresponding decomposition of the pair distribution function of the homogeneous electron gas is considered: g(r) = 1 - 1/2 [f(r)]2 - h(r) Here the one-particle density matrix n(r, r') = nf(\r-r'\) arises from the correlated momentum distribution function n(k) and h(r) is the irreducible part of g(r). In comparison with [f-degrees(r)]2 arising from the uncorrelated Hartree-Fock momentum distribution function n-degrees(k) the corresponding correlated function [f(r)]2 is slightly narrowed leading to a reduction of the exchange energy-epsilon(x). Normalization condition and virial theorem contain the mutual density dependence of the different parts of the total pair distribution function hole 1 - g(r). The situation is illustrated with the help of a simple model for the correlated momentum distribution function.