q-Gaussians and the shapes of Raman spectral lines

Abstract

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. As it will be clear from the discussion, in particular referring to (Meier, 2005), this is a very sensitive issue. Then, 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).