LiquidHe3. III. The Binding Energy and Other Properties at Zero Temperature

The binding energy of liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is estimated by separate calculations of the two-body and the three-body interaction energy. The two-body contribution is calculated by means of Brueckner theory, using a modified Brueckner-Gammel method. The approximation of a reference energy spectrum with an effective mass and quadratic momentum dependence is used for the input single-particle energy spectrum. The intermediate-state potential energies off the energy shell are chosen to be equal to zero, and the outer self-consistency requirement in the Brueckner method is neglected. A self-consistent solution is obtained, however, by the requirement that the input and the output energy spectrum for particles on the energy shell in the Fermi sea shall give the same two-body interaction energy.