Light Scattering from extended kinetic models: Monatomic ideal gases

We propose an extended kinetic model for monatomic ideal gases that replaces (in the same manner as in the Bhatnagar-Gross-Krook model) the Boltzmann collision operator with a single relaxation-time term. The model contains several position and time dependent coefficients that are determined by keeping some of the main properties of the Boltzmann description for monatomic gases of Maxwellian particles. As an application, we calculate the spectral distribution of light scattered by density fluctuations in monatomic gases by solving the linearized kinetic model equation as an initial value problem. Comparison of the theoretical results with experimental light scattering data shows that our kinetic model equation can be used in both kinetic and hydrodynamic regimes to describe light scattering experiments in monatomic gases.