Analytical expression for the convolution of a Fano line profile with a Gaussian

TL;DR

This paper derives a simple analytical expression for convolving Fano line profiles with Gaussian functions, facilitating accurate spectral line fitting in atomic and ionic photoionization studies.

Contribution

It provides a novel analytical formula involving the Faddeeva function for convolving Fano profiles with Gaussians, improving computational efficiency.

Findings

Analytical expression simplifies convolution calculations.

Efficient numerical algorithms for the Faddeeva function are applicable.

Enhances spectral analysis accuracy in atomic physics.

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.