Studies in the method of correlated basis functions. (II). Graphical analysis and integral equation methods

Techniques are introduced for accurate evaluation of the combination of overlap and Hamiltonian matrix elements required in a perturbation treatment of the uniform extended Fermi medium by the method of correlated basis functions. The correlated basis consists of Fermi-gas eigenfunctions, each modified by the same state-independent Jastrow correlation factor and normalized to unity. The cluster expansions of the required quantities are given in a diagrammatic representation, and the essential partial summations are performed by means of integral equations. The compound-graphical functions of the Fermi hypernetted-chain theory of the Jastrow ground-state trial function play a central role in the analysis. The structural results obtained are expressed most simply in terms of dressed dynamical correlation bonds and dressed effective potentials.