Fermi Liquid Properties of ³He-⁴He Mixtures

We calculate microscopically the spectrum of a ³He impurity atom moving in ⁴He, determine the Fermi-Liquid interaction between ³He atoms and then calculate the pressure and concentration dependence of the effective mass and the magnetic susceptibility. The long wavelength limit of the spectrum defines the hydrodynamic effective mass. When k ≥ 1.7 Å^-1 the motion of the impurity is damped due to the decay into a roton and a low energy impurity mode. The calculations of the Fermi-Liquid interaction are based on correlated basis functions (CBF); the relevant matrix elements are determined by the Fermi hypernetted-chain theory. Our theoretical effective masses agree well with recent measurements,^1,2 but our analysis suggests a new extrapolation to the zero-concentration limit. With that effective mass we also find a good agreement with the measured³ Landau parameter F^a₀.