Light scattering from extended kinetic models: polyatomic ideal gases

We propose an extended kinetic model for polyatomic ideal gases that replaces 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 polyatomic gases of rough spherical molecules. As an application, we calculate the spectral distribution of light scattered by density fluctuations in polyatomic gases by solving the linearized kinetic model equation as an initial value problem. Numerical results for the light scattering spectrum are derived for methane (CH4) and compared with the predictions of the extended hydrodynamic theory of Hammond and Wiggins which are in complete agreement with experimental data.