Speed-dependent effects in Doppler-free saturation spectra

We analyze the influence of the speed dependence of collisional broadening and shifting on the shape of Doppler-free saturation spectra. Our discussion is limited to the case of strong inelastic collisions when all velocity-changing collisions are also the state-changing collisions and lead only to the Lorentzian broadening of the line. We are focused on the Doppler-shifted saturation line shapes and their application for the determination of parameters describing the speed dependence in the hypergeometric and quadratic approximations commonly used in the spectroscopic databases. We provide relations between three-dimensional speed-dependent collisional broadening and shifting, used in the analysis of Doppler-broadened spectra, and two-dimensional velocity-averaged collisional broadening and shifting occurring in the Doppler-shifted saturated spectra in the quadratic approximation.