Correlation Effects in the Theory of Combined Doppler and Pressure Broadening - I . Classical Theory

A classical Fourier amplitude theory of combined Doppler and pressure broadening in the impact approximation is developed which treats phase changes due to translation and collision on an equal basis. Radiator motion is accounted for properly by includingspeed dependence in the collision frequency and velocity dependence in the distribution function for phase shifts and final velocities as the result of a collision. The resulting theory is shown to be equivalent to a previous kinetic equation formulation of the problem. Theone-perturberandclassical analogue of the quantum one-interacting-level approximations are derived. In the latter case, a simple expression for the line shape in terms of speed dependent width and shift functions is obtained without approximation. Correlation effects are investigated by means of model speed dependent width and shift functions calculated for an inverse power interaction using straight line trajectories. The model shows no departure from a Voigt profile for the r 3 interaction and for the r 6 and r I 2 interactions the resulting profile is narrower in the core than the Voigt and in general asymmetric. Analysis of correlated profiles as Voigt profiles is shown under some conditions to lead to non-linear density dependence in the width and shifts resulting in extrapolation anomalies and to significant errors in temperatures inferred from Doppler widths. Results are compared with previous work. 1. I N T R O D U C T I O N FUNDAMENTAL to an understanding of spectral line shapes is the problem of combining the effects of various phenomena that influence the line profile. The present work is concerned primarily with the combined influence of radiator-perturber collisions and radiator translational motion"-'') in the context of foreign gas broadening of optical transitions in neutral radiators. As is well known the translational motion of a radiator produces frequency shifts due to the Doppler effect and we may quasi-classically describe collisions as producing phase changes in the emitted radiation. Traditionally, one has assumed that these broadening mechanisms are statistically independent so that the line profile is described by a convolution integral (GRIEM,(") p. IO]), m I ( o ) = ID(w')I,,(o 0') dw',