Single-particle and Fermi-liquid properties of mixtures: A microscopic analysis

We calculate microscopically the properties of the dilute (Formula presented) component in a (Formula presented) mixture. These depend on both the dominant interaction between the impurity atom and the background and the Fermi liquid contribution due to the interaction between the constituents of the (Formula presented) component. We first calculate the dynamic structure function of a (Formula presented) impurity atom moving in (Formula presented) From that we obtain the excitation spectrum and the momentum dependent effective mass. The pole strength of this excitation mode is strongly reduced from the free particle value in agreement with experiments; part of the strength is distributed over high frequency excitations. Above (Formula presented) the motion of the impurity is damped due to the decay into a roton and a low energy impurity mode. Next we determine the Fermi-liquid interaction between (Formula presented) atoms and calculate the pressure and concentration dependence of the effective mass, magnetic susceptibility, and the (Formula presented) scattering phase shifts. The calculations are based on a dynamic theory that uses, as input, effective interactions provided by the Fermi hypernetted-chain theory. The relationship between both theories is discussed. Our theoretical effective masses agree well with recent measurements by Yorozu et al. [Phys. Rev. B 48, 9660 (1993)] as well as those by R. Simons and R. M. Mueller [Czech. J. Phys. 46-S1, 201 (1996)], but our analysis suggests another extrapolation to the zero-concentration limit. With that effective mass we also find a good agreement with the measured Landau parameter (Formula presented).