A refinement is made on the approximate energy expression proposed previously by Takano and Yamada for infinite zero-temperature systems of spin-1/2 fermions interacting through two-body central forces which may depend on the two-body spin states. This refinement is accomplished through incorporation of a certain part of the three-body-cluster exchange terms into the energy expression. The Euler-Lagrange equation is derived from the refined energy expression and solved numerically for liquid 3He and for neutron matter. The energy per particle for liquid 3He is in better agreement with experimental data, while the effect of this refinement is relatively small for neutron matter. The three-body cluster terms not included in the refined energy expression are evaluated perturbatively and shown to be negligibly small for liquid 3He as well as for neutron matter with central forces.
ASJC Scopus subject areas