Applied Physics and Mathematics Annotation << Back POSSIBILITIES OF THE EXTENDED WEIGHTED REGULARIZATION METHOD FOR PROCESSING SPECTROSCOPY DATA O.M. NEMTSOVA, G.N. KONYGIN The application of spectroscopic methods for studying the atomic structure of modern materials involves to address the unique mathematical methods of processing experimental data. One of the advanced, theoretically substantiated and successfully used methods for solving inverse ill-posed problems is Tikhonov’s extended method of weighted regularization. The result of application of this method for processing spectroscopic data with closely spaced weakly resolved spectral components makes to reliably separate the spectral contributions, which cannot be done by other methods. In any spectroscopic experiment, there are factors that lead to the formation of an “integral line shape”, which cannot be taken into account by the analytically. In the equation of the extended model of the inverse problem of spectroscopy, the broadening effects, using the example of Mössbauer spectroscopy, are mathematically expressed by the convolution of the function of the elementary Lorentz component and Gaussian functions, which makes it possible to process experimental data in terms of a statistical ensemble of local atomic configurations. Using the examples of processing the spectra of Fe75Si15Ge10 and Fe75Si15Al10 solid solutions, it is shown that the extended method of weighted regularization makes it possible to obtain a physically justified solution, significantly improves the quality of the spectra processing, and increases the information content of spectroscopy methods. Keywords: spectroscopy, Tikhonov’s regularization, solid solution, local atomic configuration, extended model. DOI: 10.25791/pfim.04.2023.1263 Pp. 03-12.