Correlations in fully-spin-polarized liquid 3He: Ladders, rings, and the particle-hole irreducible interaction.

We investigate the relative contribution of ladder and ring diagrams to the single-particle self-energy in fully-spin-polarized liquid He ( He~). Ladder diagrams are summed to all orders of the bare HeHe interaction using the Galitskii-Feynman-Hartree-Fock (GFHF) analysis. Previous studies of He, using GFHF analysis, have neglected the part of the GFHF self-energy coming from the correlation potential, V, . These calculations produced ground-state energies in fair agreement with values obtained from variational Monte Carlo (VMC) calculations. However, properties such as Landau parameters, which are directly related to long-range correlations, tend to differ considerably from known values. In the present work we have evaluated V„and found it to have an appreciable effect on the single-particle excitation energies, c(k) and the ground-state energy: Including V„significantly reduces the ground-state energy. As a further refinement over previous GFHF calculations, we have used a more accurate center-of-mass momentum, P, dependence for the Galitskii-Feynman t matrix in the self-energy calculation. Again we find an undesirably large decrease in the ground-state energy. Finally, upon including a contribution from a summation of ring diagrams, we find a ground-state energy that is once again in fair agreement with the VMC values. The ring diagrams are driven by a local particle-hole interaction obtained by the method of correlated basis functions (CBF}. Ring diagrams are then summed within a random-phase approximation. Our final c(k) is used to calculate the particle-hole irreducible interaction I~ z. In the long-wavelength limit we find that our I~ h is in much better agreement with the CBF Ip Q when our c( k ) includes contributions from V„,X&, and the refined self-energy calculation.