Reflectivity spectra as absorption ones -- is it correct ?

TL;DR

This paper develops approximate models for X-ray and Mössbauer reflectivity in the external reflection region, showing when reflectivity spectra can be considered as absorption spectra and highlighting potential distortions affecting spectroscopic analysis.

Contribution

It introduces simplified expressions for reflectivity in specific cases and analyzes conditions under which R-spectra can be accurately treated as absorption spectra, including effects of dispersive distortions.

Findings

Reflectivity can be proportional to the imaginary part of susceptibility in certain conditions.

Dispersive distortions significantly affect R-spectrum shape at larger nonresonant absorption.

Using absorption-based software for R-spectra analysis can lead to inaccuracies.

Abstract

Approximate expressions for X-ray resonant and M\"ossbauer reflectivity in the total external reflection region are developed for the limiting cases of a semiinfinite mirror with a small resonant addition to the total susceptibility and for the case of an ultrathin resonant layer. It is shown that in this region the reflectivity can really show the linear dependence on the imaginary part of resonant susceptibility, therefore in these cases the consideration of reflectivity spectra (R-spectra) as absorption resonant spectra, undertaken in several experimental works, can be justified. However, we have selected several effects producing essential dispersive distortions of the R-spectrum shape even for very small grazing angles. It has been shown that the dispersive corrections to the R-spectrum shape are mostly essential if the nonresonant absorption is relatively large. Model calculations demonstrate that the quantitative spectroscopic information extracted from R-spectra by using the software developed for absorption spectra can be inaccurate.