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The correlation energy of the homogeneous three-dimensional interactingelectron gas is calculated using the variational and fixed-node diffusion MonteCarlo methods, with trial functions that include backflow and three-bodycorrelations. In the high density regime the effects of backflow dominate overthose due to three-body correlations, but the relative importance of the latterincreases as the density decreases. Since the backflow correlations vary thenodes of the trial function, this leads to improved energies in the fixed-nodediffusion Monte Carlo calculations. The effects are comparable to those foundfor the two-dimensional electron gas, leading to much improved variationalenergies and fixed-node diffusion energies equal to the release-node energiesof Ceperley and Alder within statistical and systematic errors.Comment: 14 pages, 5 figures, submitted to Physical Review

Effects of backflow correlation in the three-dimensional electron gas: Quantum Monte Carlo study