Long-range correlations in fermi fluids

Abstract

Here the model wave function ~ is taken to be the ground-state function of a gas of A-independent fcrmions in a volume ~ with the particle density ~ = A / Q VkF/6X'.a ~ is the degree of degeneracy of the single-particle states, and k F the Fermi wave number. The pair correlation function ](r) is elmsen to incorporate properly the spatial correlations of the system. The energy expectation value with respect to the test wave function (l) (or other ground-state properties of interest) can be computed by means of a (truncated) cluster expansion, for example the Iwamoto-Yamada (IY) expansion (~) or its factorized version (3), or the power series (PS) expansion (4). According to the expansion tcchnique used, several classification schemes for the higher-order cluster contributions have been established. Truncating the cluster expansion of the energy expectation value one has, however, to be aware of the possibility that the approximation obtained is no longer bounded from below for sufficiently long-ranged pair correlation functions. This difficulty forbids an optimization of ](r) by nleans of a free variation. To overcome this problcnl, subcouditions (5-7) on the pair correlation function have been investigated in order to keep the (, smallness parameter ,~ ~ : = ~f~(r)dr of the expansion finite. Recently, a close study of the different cluster expansions showed that the PS classification (i.e. the ordering of the cluster contributions with respect to the number of correlation factors ~(r) involved) cancels order by order divergent portions (s) and gives