Dicke Narrowing Reduction of the Doppler Contribution to a Line Width

In the simplest kinetic models of collisional narrowing or reduction of the Doppler contribution to a spectral line width, the narrowing process is related to the usual diffusion constant of transport theory. Dicke narrowing requires a correlation between the pre- and post-collisional absorber or emitter electric dipole moment. Pressure broadening on the other hand results from at least a partial destruction of this correlation so that in general pressure broadening and Dicke narrowing are statistically dependent on and correlated with each other. It follows that a spectroscopic diffusion constant is required. A classical phase description (which is easily converted to a semiclassical one) is used here to derive a kinetic equation for which the approximate line shape is obtained by It velocity moment method. The spectroscopic diffusion constant closely resembles the Chapman-Enskog first approximation for the diffusion constant but has mixed in an extra function (the memory) which represents the correlation between collision-induced changes of the dipole moment and velocity changes and the correlation between the pre- and post-collision electric dipole moment. Dicke narrowing can be used to obtain information about the line broadening amplitude SB(b, w) for strong velocity-changing collisions. The Galatry ('weak' collision) and 'strong' collision line-shape functions are obtained as different cutoff approximations in the velocity moment analysis. The present analysis, however, is not limited to specifically weak or strong collisions. The two line-shape formulae are shown to be virtually identical sufficiently far from the line centre and at sufficiently high densities. Convenient, approximate analytical formulae for the half-width are obtained using two different definitions.