Kinetic energy and the Born-Green-Yvon method for fermion quantum fluids

Abstract

The Born-Green-Yvon (BGY) equations for two-body distribution functions of fermion-Jastrow many-body trial functions are derived using a diagrammatic method. Also derived are the Jackson-Feenberg and Pandharipande-Bethe expressions for the kinetic energy of this function in terms of partial two- and three-body distribution functions. Simple approximations for these three-body functions are then used in the BGY equations and the kinetic energies and are solved for the ground state of liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$.