Bayesian inference theory applied to hyperfine parameter distribution extraction in Mössbauer spectroscopy

We present an effective direct extraction method for hyperfine parameter distributions based on Bayesian inference theory with free-form model and give an example of application to quadrupole splitting distribution analysis in an Fe-57 Mössbauer spectrum of an Fe³⁺-chlorite. The technique gives a unique solution to the distribution with arbitrary shape and is not sensitive to the elemental doublet parameters. In addition full error analysis of the distribution is obtained for the first time in Mössbauer spectroscopy.