Cluster expansion of the distribution functions for a ground state Fermi system

Abstract

The spin-averaged Slater sum of the fermion system is expanded in terms of the square of the ground state wavefunction of a boson system and the "antisymmetry" Ursell function. This expansion is used to obtain the cluster series for the radial distribution function of the fermion system in terms of (−C⁽ⁿ⁾/S), where C⁽ⁿ⁾ is sum of chains of (−f/S) and (−fh^B₂/S) bonds. The series is further expressed in a more compact form using a function L⁽ⁿ⁾ defined by Eq. (55), and the "modified" FHNC approximation for the radial distribution function is presented.