Correlations in fully-spin-polarized liquid sup 3 He: 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 {sup 3}He ({sup 3}He{sup {up arrow}}). Ladder diagrams are summed to all orders of the bare {sup 3}He-{sup 3}He interaction using the Galitskii-Feynman-Hartree-Fock (GFHF) analysis. Previous studies of {sup 3}He{sup {up arrow}}, using GFHF analysis, have neglected the part of the GFHF self-energy coming from the correlation potential, {ital V}{sub co}. 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 {ital V}{sub co} and found it to have an appreciable effect on the single-particle excitation energies, {var epsilon}({ital k}) and the ground-state energy: Including {ital V}{sub co} significantly reduces the ground-state energy. As a further refinement over previous GFHF calculations, we have used a more accurate center-of-mass momentum, {ital P}, dependence for the Galitskii-Feynman {ital 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 {var epsilon}({ital k}) is used to calculate the particle-hole irreducible interaction {ital I}{sub {ital p}-{ital h}}.