CBF perturbation corrections to the Jastrow ground-state of the electron gas

Abstract

We have reported in this paper the first calculations for the correlation energy within the combined FHNC variational-CBF scheme. The energy corrections turn out to be rather small and-with the exception of a somewhat uncomfortable feature at very high densities- of the expected size. In particular the exact result for the high density limit gives another indication for the efficiency of our approach.

Let us conclude with some remarks on the future prospects of applications of the CBF approach in the electron gas problem. Clearly, it is feasible to include higher-order perturbation corrections and three-body correlations. It should be kept in mind, however, that the CBF corrections to the correlation energy are already smaller than the elementary diagram contributions to the variational correlation energy, and the uncertainty arising by different choices of the Jastrow function appears to be of the same order of magnitude. If a more accurate computation of the correlation energy should be desired, it should be accompanied by a renewed attack on those aspects of the variational problem mentioned above.

The accompanying paper [9] has also explained why the 2p-2h CBF corrections are so small for state-independent interactions. This is due to the fact that the Fermi-sea average of the 2p-2h interactions is made to vanish by the optimization of the Jastrow function.

Significant contributions are to be expected, however, for quantities which do not involve Fermi-sea averages of the effective interactions. The Fermi-liquid parameter calculations of ref. [9] are an obvious starting point for future investigations.

This research was supported, in part, by the U. S. Dept. of Energy under Contract No. DE-AC02-76ER13001 and by the Deutsche Forschungsgemeinschaft.