The Fitted q-Gaussian Function, from Voigt Profile to Kubo Lineshape

Several previously discussed cases have shown that the q-Gaussian Tsallis functions can be used for fitting the bands of Raman spectra. Here, considering an article by Thibault et al., 2002, we can add the case of the Raman Q branch of carbon monoxide, for mixtures with Argon at different temperatures. In Thibault et al., a plot is available for the Q(5) line with a fitted Voigt function. A q-Gaussian Tsallis function can be used for fitting this line too. We will note that the fitted q-Gaussian has the wings which are not Lorentzian. At the same time, the wings are not Gaussian. Besides the use of q-Gaussians, a discussion will be proposed about the time correlation functions related to different line shapes (q-Gaussian, Egelstaff-Schofield, Kubo, BWF, Voigt, speed-dependent Voigt, Galatry, Rautian, HTP). Some of these line shapes have been proposed for the high-resolution spectroscopy of gases; however, their knowledge can be relevant also for the condensed matter spectroscopy.