Experimental test of the quadratic approximation in the partially correlated speed-dependent hard-collision profile

Abstract

We report on the outcomes of a specific study on the quadratic approximation in the partially correlated speed-dependent hard-collision (pC-SDHC) model, which is currently the recommended profile to replace the Voigt convolution for the shape of an isolated line, when perturbed by neutral gas-phase molecules. In particular, we compared the quadratic approximation with the hypergeometric dependence of the collisional relaxation rate on the absorber velocity by using high-quality ${\mathrm{H}}_{2}^{18}\mathrm{O}$ absorption spectra, in coincidence with three vibration-rotation transitions of the ${\ensuremath{\nu}}_{1}+{\ensuremath{\nu}}_{3}$ band, at 1.39 $\ensuremath{\mu}$m, also by looking for possible differences in the retrieved parameters. The pC-SDHC profile was found to be quite robust, regardless of the choice of the particular speed dependence. The pressure broadening and shifting parameters, retrieved by using the quadratic and hypergeometric versions, were found to be fully consistent, provided that the velocity-changing collision frequency ${\ensuremath{\nu}}_{\text{vc}}$ was considered as a free parameter. Similarly, the integrated absorbance was found to be completely unaffected by the choice of the speed dependence, in the entire pressure range we have explored. It must be noted, however, that the velocity-changing collision frequency resulted to be largely overestimated compared to the expected one when using the quadratic approximation. Moreover, the ${\ensuremath{\nu}}_{\text{vc}}$ values from the quadratic approximation are always significantly larger than those of the hypergeometric model.