q-Gaussian Tsallis Line Shapes and Raman Spectral Bands

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 line shapes most used to fit the spectral bands. Therefore, we will propose q-Gaussians with the aim of comparing the resulting fit analysis with data available in literature. As it will be clear from the discussion, this is a very sensitive issue. We will also provide a detailed discussion about Voigt and pseudo-Voigt functions and their role in the line shape modeling of Raman bands. We will show a successfully comparison of these functions with q-Gaussians. The role of q-Gaussians in EPR spectroscopy (Howarth et al., 2003), where the q-Gaussian is given as the "Tsallis lineshape function", will be reported. Two examples of fitting Raman D and G bands with q-Gaussians are proposed too. Torino, 19 March 2023.