INELASTIC LIGHT SCATTERING FROM THERMAL FLUCTUATIONS IN GASES by NOEL

We have studied the Brillouin spectrum of light scattered by the dilute monatomic one component gases xenon and helium and by the xenon-helium binary gas mixture. In a one component monatomic gas the scattered light spectrum for a scattering process with momentum transfer, K, and energy transfer, w, is proportional to the power spectrum, S(K, W), of fluctuations in the density of the gas. In a dilute monatomic gas this spectrum should be obtainable from the Boltzmann equation. In 1959 Gross and Jackson proposed a method of solution of the Boltzmann equation (the kinetic model procedure) whereby one could calculate the space-time dependence of phenomena of arbitrary frequency, w, and wavelength, A, i. e. both in the kinetic regime where A is small compared to the molecular mean free path, and in the hydrodynamic regime where there are many collisions over the length A . Recently, Sugawara, Yip, and Sirovich have applied the kinetic model procedure to the calculation of the density fluctuation spectrum of the Maxwell molecule and hard sphere gases. We have measured the de s4ty flyctuation spectrum, S(K, ), in xenon gas at T = 22 0 C, K = 2 x 10 cm , through the kinetic-hydrodynamic transition. We find the spectra calculated via the kinetic model procedure for both Maxwell molecules and hard spheres to be in excellent agreement with the measured spectra. This result shows the kinetic model procedure to be an accurate method of solution of the Boltzmann equation and is evidence of the insensitivity of time dependent phenomena in a dilute system to the exact form of the intermolecular potential. We have studied non-hydrodynamic behavior in the heliumxenon binary gas mixture with xenon dilute. Because of the large molecular mass ratio and scattering cross section ratio of xenon to helium, the light scattered by the xenon may be separated from the total scattered light spectrum. We have studied the spectrum of the light scattered by the xenon as a function of helium pressure. At low helium pressure xenon atoms are in free flight over the length 21r /K, and the resulting scattered light spectrum is Gaussian. At high helium pressure the xenon atoms diffuse over the length 21T/K and the spectrum is Lorentzian. The study of the Gaussian to Lorentzian evolution of the scattered light spectrum shows that the Fokker-Planckmodelis appropriate to approximate