The collective excitati on spectrum in the case of two interacting Fermi- fields is considered, The main approximation is the high density limit in which the correlation energy was calculated. (auth)
Results for the diagonal element of the second-order density matrix (pair function) and for the momentum distribution of an interacting electron gas are presented. In the low density limit, it is shown that, to a similar degree of approximation, the first-order density matrix and hence the momentum distribution may be obtained. In the highdensity problem, the pair function has also been calculated using the Green's function approach. From the information available in these high and low density limits, the range of usefulness of the concept of the Fermi surface in an interacting electron gas is discussed. Also, results of varia. tional calculations on the stability of Cverhauser spindensity waves in metals are reported. It is concluded that such waves reduce the energy below the Hartree-Fock value only when the interaction becomes very strong, or equivalently when the density is very low. Some preliminary work on the correlation problem in a non-uniform electron gas is also briefly discussed. (auth)