We discuss spectral profiles from the point of view of a Boltzmann transport relaxation equation. We present an exact solution to the Fokker-Planck-type equation in the soft collision limit for the special case of a quadratic speed-dependent collisional width and shift of the line. The resultant spectral profile is compared to several related, more approximate expressions reported previously.
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Ciuryło et al. (2001) studied this question.