Intercollisional memory effects and short-time behavior of the velocity-autocorrelation function from translational spectra of liquid mixtures

We discuss here the intercollisional memory effects which have been detected in the low-frequency region of the absorption spectra induced by collisions in dilute solutions of para-${\mathrm{H}}_2$, He, and Ne in liquid argon. The theories of gaseous mixtures are shown to be inadequate to describe the spectra in liquids. Then we calculate the low-frequency part of the translational absorption spectrum for an argon crystal doped with impurities. The results of such a calculation for the solid are compared with the experimental data on liquid solutions and with the behavior predicted by the gaseous theories. We also show that from the induced-dipole-moment autocorrelation function, as obtained from the experimental data, it is possible to determine the short-time behavior of the force and velocity-autocorrelation functions of the impurity in the liquid. In particular we obtain the mean-square force $〈F^2〉$ acting on the impurity and $〈{\dot{F}}^2〉$. The derived values of $〈F^2〉$ and $〈{\dot{F}}^2〉$ are compared with those estimated with the help of the radial-distribution function of the liquid mixtures.