Spectrum of Density Fluctuations in Gases

The spectrum of density fluctuations in a simple gas is calculated by solving the linearized Boltzmann equation as an initial-value problem. The analysis is based on the method of polynomial expansion and on the use of generalized kinetic models. The numerical convergence of both types of solutions is studied, and it is shown that the method of kinetic models is capable of giving very accurate solutions to the Boltzmann equation at any wavelength to mean-free-path ratio. Explicit results are obtained for two repulsive interactions, the rigid-sphere potential and the Maxwell molecule potential. It is found that density fluctuations are not very sensitive to the details of the repulsive part of the intermolecular interaction.