New Simple Method to Analyze Mildly Gaussian-Convolved Lorentzian Lines with the Aid of DISPA Data

Abstract

A new and simple method, not based on numerical fitting, to analyze mildly Gaussian-convolved Lorentzian isolated nonoverlapped lines in any spectroscopy, with the aid of DISPA (DISPersion vs. Absorption) data, is presented. The method is based on a model of the dispersion line which is obtained by taking the Hilbert transform of a previously published approximate expression for the absorption Voigt profile. The resulting DISPA pair is valid in the interval α, where α is a parameter that measures the relative Lorentzian (ΓL) and Gaussian (ΓG) full width at half-maximum (FWHM) contributions to the Voigt profile. As an example of an application of the method, a deconvolution of the potassium–ammonium solution electron paramagnetic resonance (EPR) line is performed. This deconvolution produces the Lorentzian and Gaussian contributions to the line. The deconvolution operation is done after obtaining a list of DISPA values for this line. The resulting values of the Lorentzian and Gaussian FWHMs are then compared with those obtained after deconvolving the line by fitting the spectral data with both the exact and approximate expressions for the Voigt profile. The method may be used in any spectroscopy in which the spectral lines are not overlapped and can be represented by Voigtians with a small Gaussian component and with a very low degree of asymmetry.