A study of the single-moment, two-moment and multilevel descriptions of depolarized Rayleigh light scattering in molecular gases

Abstract

Derivations of appropriate kinetic-theory expressions for the depolarized Rayleigh (DPR) spectral lineshape function and its corresponding time auto-correlation function are presented for the single-moment, two-moment and multilevel descriptions of light scattering in dilute polyatomic gases. A comparison is given between the predictions of these descriptions, using close-coupled scattering calculations of the relevant reorientation collision cross-sections for HD and N₂ interacting with He. The role of inelastic reorientation cross-sections is elucidated. The decay of fluctuations in the non-equilibrium average of the microscopic orientational polarization (4j ² - 3)^-1 , which is responsible for the DPR spectrum, is sensitive to the transfer of this polarization between the rotational levels of HD (or N₂) as the result of inelastic molecule-He reorientation collisions. It is shown that the single-moment description is adequate only for HD at very low temperatures (never for N₂), and that the two-moment description yields results that agree quantitatively with the full multilevel description for temperatures at which the molecules contributing to the light scattering are thermally distributed over rather few rotational levels. For HD this condition is satisfied for temperatures as high as 300 K, but for N₂ it is not satisfied even for temperatures as low as 50 K.