A modified Boltzmann kinetic equation for line shape functions

Abstract

The shape of an isolated spectral transition is analyzed in terms of an approximation to the Waldmann-Snider kinetic equation. This equation is written in the form of a drift and collision operator acting on a density matrix. With the use of the sphericalll.pproximation, the collision operator is subdivided into an elastic Boltzmann-like collision term, an inelastic loss term, and a dephasing term. The Boltzmann-like term is responsible for Dicke narrowing of spectral lines, the inelastic loss term leads to line broadening and the dephasing term may contribute both to line broadening and shifting. Simple approximations to these terms are powerful enough to account for some of the details of experimental1ine shapes such as asymmetrical deviations from a Lorentzian line shape. Model numerical calculations are carried out assuming classical scattering potentials ofthe form 1/1'" in the Boltzmann-like term and single complex frequencies for the other two. It was found that as long as the density was scaled to give the same diffusion constant, the exact form of the scattering cross section had little effect on the final line shape..

Velocity-changing collisions in pure H2 and H2-Ar mixture

“…It is also convenient 19,33,52,53 to introduce the operator S f VC which is related to the operatorŜ VC in the following wayŜ…”

“…54 This operator was used for the study of Dicke narrowed spectral lines. 19,24 Collision kernels can be also derived from CMDS as done in Refs. 51 and 55 where details of calculations can be found.…”

“…A more advanced model describing velocity-changing collisions, which allows to properly incorporate the mass ratio of colliding pair is the so called billiard-ball model or rigid-spheres model. 19,33,34 In this approach, the molecular potential is modelled by considering only the repulsive wall of two rigid spheres having masses m 1 and m 2 . The collision kernel for the BB model can be expressed analytically following Liao, Bjorkholm, and Berman 34…”

“…calculations based on quantum mechanical scattering and solving transport/relaxation equation [19][20][21] or based on classical molecular dynamic simulations (CMDS) 22,23 can significantly reduce the number of approximations for spectra evaluation.…”

“…At present, to the best of our knowledge, the most realistic models describing velocity-changing collisions applicable in line shape calculation 19,24,25 and used for fitting of experimental data [25][26][27][28][29][30][31][32] are the billiard-ball (BB) model 19,33,34 and a bit more general Blackmore model, 19,35 which assumes repulsive inverse-power potential. The most important advantage of the BB model is that it allows to take into account the speed-dependence of frequency of velocity-changing collisions as well as the speed-and direction-changing collisions for a given perturber/absorber mass ratio in a proper way.…”