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 spherical approximation, 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 experimental line shapes such as asymmetrical deviations from a Lorentzian line shape. Model numerical calculations are carried out assuming classical scattering potentials of the form 1/rn 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.