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

Abstract

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.The three-body contribution to the binding energy is estimated separately by methods originally developed for nuclear-matter calculations by Bethe and collaborators. Only the $S$-wave is properly taken into account. Third-order diagrams are also estimated separately.For the Yntema-Schneider potential given by Brueckner and Gammel, we obtain a total binding energy for liquid $^{3}\mathrm{He}$ of -1.0\ifmmode^\circ\else\textdegree\fi{}K per particle, which is in general agreement with other calculations. For the Frost-Musulin potential given by Bruch and McGee, we get -2.0\ifmmode^\circ\else\textdegree\fi{}K per particle, which is closer to the experimental value.Also, other low-temperature properties, such as the compressibility, the coefficient of thermal expansion, and the magnetic susceptibility, are estimated, with results in fair agreement with experimental values. The theoretical results are: 4.3% per atmosphere for the compressibility, $\ensuremath{-}0.10T$ (${\mathrm{\ifmmode^\circ\else\textdegree\fi{}}\mathrm{K})}^{\ensuremath{-}1}$ ($T$ in \ifmmode^\circ\else\textdegree\fi{}K) for the coefficient of thermal expansion, and $\ensuremath{\approx}10$ for the magnetic susceptibility ratio. The quasiparticle effective mass, or equivalently the linear term in the temperature dependence of the specific heat, cannot be estimated very well with our methods.