  The correlation energy of the homogeneous three-dimensional interacting
electron gas is calculated using the variational and fixed-node diffusion Monte
Carlo methods, with trial functions that include backflow and three-body
correlations. In the high density regime the effects of backflow dominate over
those due to three-body correlations, but the relative importance of the latter
increases as the density decreases. Since the backflow correlations vary the
nodes of the trial function, this leads to improved energies in the fixed-node
diffusion Monte Carlo calculations. The effects are comparable to those found
for the two-dimensional electron gas, leading to much improved variational
energies and fixed-node diffusion energies equal to the release-node energies
of Ceperley and Alder within statistical and systematic errors.
