LiquidHe3. IV. Effective Mass, Rearrangement Energy, Magnetic Susceptibility, and Transport Coefficients

Using the reaction matrix or $G$ matrix obtained by Brueckner theory for liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, rearrangement energy corrections to the so-called single-particle energy are evaluated. The corrected single-particle energy at the Fermi surface is fairly close to the binding energy obtained by earlier calculations. This satisfies roughly the Hugenholtz-Van Hove separation energy theorem. The density dependence of the $G$ matrix, or the derivatives with respect to the Fermi momentum, are evaluated numerically, and properties like the effective mass and the magnetic susceptibility are estimated. The calculated values are in fairly good agreement with experimental results, giving an effective mass of 2.0 to 2.5, and a magnetic susceptibility ratio of 7 to 40. The experimental values are 3.1 and 9. Also transport coefficients, i.e., viscosity, thermal conductivity, and spin diffusion, are estimated after identification of the $G$ matrix with the scattering amplitude in the formulas developed by Abrikosov and Khalatnikov, and by Hone. The agreement with experimental results is not very good; the difference is a factor of 1.5 to 10.