Deconvolution of Transmission Mössbauer Spectra Using Conjugate Gradient Method

A numerical method to extract the absorber resonance cross-section from the transmission Mössbauer spectrum has been presented. The convolution equation which relates to both of the transmission spectrum and the cross-section is expressed by linear algebraic equation and solved by conjugate gradient method. Applying this method to the examples simulated numerically, the resonance cross-section spectra have been successfully reproduced. Present method is powerful to determine the intensities and their ratios of the absorption lines. The effects due to the statistical fluctuations of the data and the non-resonant radiation have been also discussed.