Analytical Formula for the Relation between the Experimental and Theoretical Parameters of the Tsallis Spectral Line

Abstract

An exact analytical formula is obtained that relates the experimental and theoretical parameters of the spectral line described by the Tsallis function, which includes the Gaussian, Lorentzian, line shapes intermediate between them, and super-Lorentzian as special cases. The procedure for the numerical calculation of the theoretical parameters of the line shape is studied by the example of electron spin resonance spectra. The effect of complicating experimental factors, including the noise and the analog signal digitization discreteness, on the accuracy of determining the theoretical Tsallian parameters is examined. It is shown that the proposed method for determining the theoretical parameters of the spectral line is not inferior in accuracy to the method for minimizing the root-mean-square error functional. It is predicted that the new approach can be used as an alternative to the available spectral line shape analysis techniques.