Condensed Matter Physics, 1999, vol. 2, No. 2(18), p. 319-328, English

Authors: K.Schorkhuber, E.Krotscheck (Institut fur Theoretische Physik, Johannes Kepler Universitat A 4040 Linz, Austria), J.Paaso, M.Saarela (Department of Physical Sciences, Theoretical Physics, University of Oulu, FIN-90570 Oulu, Finland), R.Zillich (Institut fur Theoretische Physik, Johannes Kepler Universitat A 4040 Linz, Austria)

We calculate microscopically the properties of $^3$He impurity atoms in $^3$He-$^4$He mixtures, including the spectrum of a single particle and the Fermi--Liquid interaction between $^3$He atoms. From these, we determine the pressure and concentration dependence of the effective mass and the magnetic susceptibility. The long wavelength limit of the single--particle spectrum defines the hydrodynamic effective mass. When $k\geqslant 1.7 $\AA$^{-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) perturbation theory; the relevant matrix elements are determined by the Fermi hypernetted--chain summation method. Our theoretical effective masses agree well with recent measurements \cite{Yorozu93,SimonsLT21} but our analysis suggests a new extrapolation to the zero-concentration limit. With that effective mass we also find a good agreement with the measured \cite{APCT76} Landau parameter $F_0^a$.

Comments: Figs. 4, Refs. 19, Tabs. 1.

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