Bayesian Inference on Hamiltonian Selections for Mössbauer Spectroscopy

Mössbauer spectroscopy, which provides knowledge related to electronic states in materials, has been applied to various fields such as condensed matter physics and material sciences. In conventional spectral analyses based on least-square fitting, hyperfine interactions in materials have been determined from the shape of observed spectra. In conventional spectral analyses, it is difficult to discuss the validity of the hyperfine interactions and the estimated values. We propose a spectral analysis method based on Bayesian inference for the selection of hyperfine interactions and the estimation of Mössbauer parameters. An appropriate Hamiltonian has been selected by comparing Bayesian free energy among possible Hamiltonians. We have estimated the Mössbauer parameters and evaluated their estimated values by calculating the posterior distribution of each Mössbauer parameter with confidence intervals. There is no previous research about Bayesian inference of Mössbauer spectra such as our method. We have also discussed the characteristics of the posterior distribution specific to the Mössbauer spectrum and the accuracy of the spectral analyses to elucidate the noise intensity dependence of numerical experiments.