Analytical expression for the convolution of a Fano line profile with a gaussian. (November 2018)

• Record Type: Journal Article
• Authors: Schippers, S.
• Is Part Of: Journal of quantitative spectroscopy & radiative transfer. Volume 219(2018)
• Page Start: 33
• Page End: 36
• Publication Date: 2018-11
• Subjects: Line shapes -- Fano profile -- Convolution -- Special functions; 32.70.Jz -- 02.30.Gp; Spectrum analysis -- Periodicals; Radiation -- Periodicals; Analyse spectrale -- Périodiques; Rayonnement -- Périodiques; Radiation; Spectrum analysis; Periodicals; 543.0858
• DOI: 10.1016/j.jqsrt.2018.08.003
• Languages: English
• ISSNs: 0022-4073

Abstract

Highlights: Fano line shapes are frequently encountered in atomic spectroscopy. Line-profile fitting to experimental data requires a convolution with an experimental window function. In the past, the convolution was carried out by using either slow numerical or inaccurate approximation procedures. Here an analytic formula for the convolution of a Fano profile with a Gaussian is derived. The formula involves the Faddeeva function for which efficient and accurate algorithms are available. Abstract: Asymmetric Fano line profiles are frequently encountered, e. g., in the photoionization spectra of atoms and ions. For the fitting of spectral line profiles to experimental spectra the line profiles have to be convolved with the experimental window function. The latter is often taken to be a gaussian. It is shown that the convolution can be represented by a rather simple analytic expression involving the Faddeeva function for the evaluation of which efficient and accurate numerical algorithms are available.