Fourier-transform method for accurate analysis of Moessbauer spectra

We report a simple analytic form for the convolution integral in transmission Moessbauer spectroscopy allowing accurate representation of the line shape even for very thick absorbers (t = 10), and permitting easy fitting to the true line-shape function. This representation permits the accurate determination of all Moessbauer-effect (ME) parameters, including position, width, cross section, and interference. This analytic method can be applied to deconvolute accurately information contained in either source or absorber, and an explicit analytic form for the emission and absorption Fourier transforms is given. We show that from the asymptotics of the line shape, it is possible to determine all line-shape parameters, and that line-shape asymptotics can circumvent short-ranged hyperfine or instrumental broadening contributions to the observed spectrum. A formula for the correction to the line shape caused by source self-absorption is given, and it is shown that when there is significant source resonance self-absorption a ''good'' fit to data, judged by a chi-squared analysis, can yield completely wrong ME line-shape parameters. We find an equation for the dependence of the area under the absorption curve and the resonance peak height, and give its explicit dependence on the interference parameter and source broadening parameters. Although these effects have been neglected in earlier work, their contribution may be of order 10% in many cases of interest