q-Gaussians and the shapes of Raman spectral lines

q-Gaussians are probability distributions having their origin in the framework of Tsallis statistics. A continuous real parameter q is characterizing them so that, in the range 1 < q < 3, the q-functions pass from the usual Gaussian form, for q close to 1, to that of a heavy tailed distribution, at q close to 3. The value q=2 corresponds to the Cauchy-Lorentzian distribution. This behavior of q-Gaussian functions could be interesting for a specific application, that regarding the analysis of Raman spectra, where Lorentzian and Gaussian profiles are the most commonly used line shapes to fit the spectral bands. Therefore, we will discuss q-Gaussians with the aim of comparing the resulting fit analysis with data available in literature. In particular, we will discuss results given in a recently proposed analysis of carbon-based materials, obtained by means of mixed Gaussian and Lorentzian line shapes, defined as GauLors (Tagliaferro et al., 2021).