q-Gaussian Tsallis Functions and Egelstaff-Schofield Spectral Line Shapes

q-Gaussian Tsallis Functions and Egelstaff-Schofield Spectral Line Shapes

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Author(s)

Author(s): Amelia Carolina Sparavigna

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DOI: 10.18483/ijSci.2673 25 104 47-50 Volume 12 - Mar 2023

Abstract

In this article we will discuss the Egelstaff-Schofield line shapes, as used in Raman spectroscopy, and their fit by means of q-Gaussian Tsallis functions. 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, 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 allows the q-Gaussian function to properly mimicking the Egelstaff-Schofield line shape, which has been introduced to fit the bands of first-order Raman scattering in ionic liquids. This line shape is based on a modified Bessel function of the second kind. Moreover, since the Fourier transform of the Egelstaff-Schofield line shape is given by a simple analytical expression, we can use this expression as an easy substitute for the Fourier transform of the q-Gaussian function.

Keywords

q-Gaussian distribution, Gaussian distribution, Cauchy distribution, Lorentzian distribution, Voigt distribution, Egelstaff-Schofield line-shape, Raman spectroscopy, EPR spectroscopy

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International Journal of Sciences is Open Access Journal.
This article is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License.
Author(s) retain the copyrights of this article, though, publication rights are with Alkhaer Publications.

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