Different widths of resonant lines in the Mössbuaer spectrum as the result of multidimensional Gaussian distribution

In the application of Mössbauer spectroscopy to complex materials distributions of hyperfine parameters are regularly utilized in data processing. Distributions are required due to existence of a huge number of different local positions of Fe ions with varying nearest environment. Thus, the Mössbauer spectrum should contain a lot of different corresponding subspectra. It often leads to a problematic independent determination of individual sites. In simplest case it could lead just to an increase of the width of resonant lines due to normal distribution of hyperfine parameters. However, they could appear to be correlated. In such case the shape of the spectrum will change, requiring more complex model to describe it. In this work such a model was developed and compared to already existed approaches.