Accurate quantitative analysis of Mössbauer spectra displaying thickness effects requires the consideration of the so-called transmission integral when modeling the spectral shape. Whereas this is straightforward when the correct model for the decomposition of the absorber's nuclear resonance absorption cross-section into individual components is a priori known, in the absence of such knowledge and notably in the presence of hyperfine parameter distributions with an unknown profile, the so-called model-independent evaluation methods could be used to fit the spectra. However, the methods available for this purpose were developed for the analysis of spectra for which the thin absorber approximation is valid, and thus they do not take the sample thickness and related effects into account. Consequently, in order to use them for spectra displaying thickness effects, their usage needs to be generalized by combining them with transmission integral fitting. A new algorithm realizing such a generalized version of the Hesse-Rübartsch model-independent evaluation method was developed recently as an integral part of the MossWinn program. In the present work, the working principle of the newly developed algorithm is described in details along with examples illustrating the capabilities of the method for the case of 57Fe Mössbauer spectroscopy.

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