SINGLE-PARTICLE AND FERMI-LIQUID PROPERTIES OF HE-3-HE-4 MIXTURES - AMICROSCOPIC ANALYSIS

We calculate microscopically the properties of the dilute He-3 compone nt in a He-3-He-4 mixture. These depend on both the dominant interacti on between the impurity atom and the background and the Fermi liquid c ontribution due to the interaction between the constituents of the He- 3 component. We first calculate the dynamic structure function of a He -3 impurity atom moving in He-4. From that we obtain the excitation sp ectrum 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 ov er high frequency excitations. Above k greater than or equal to 1.7 An gstrom(-1) 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-li quid interaction between He-3 atoms and calculate the pressure and con centration dependence of the effective mass, magnetic susceptibility, and the He-3-He-3 scattering phase shifts. The calculations are based on a dynamic theory that uses, as input, effective interactions provid ed by the Fermi hypernetted-chain theory. The relationship between bot h theories is discussed. Our theoretical effective masses agree well w ith recent measurements by Yorozu et nl. [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 th e zero-concentration limit. With that effective mass we also find a go od agreement with the measured Landau parameter F-0(a). [S0163-1829(98 )05142-X].