The Coherent Forward Scattering Amplitude in Transmission and Grazing Incidence M\"ossbauer Spectroscopy

The theory of both transmission and grazing incidence M\"ossbauer spectroscopy is re-analyzed. Starting with the nuclear susceptibility tensor a common concise first order perturbation formulation is given by introducing the forward scattering amplitude into an anisotropic optical scheme. Formulae of Blume and Kistner as well as those of Andreeva are re-derived for the forward scattering and grazing incidence geometries, respectively. Limitations of several previously intuitively introduced approximations are pointed out. The grazing incidence integral propagation matrices are written in a form built up from 2x2 matrix exponentials which is particularly suitable for numerical calculations and practical fitting of both energy domain (conventional source experiment) and time domain (synchrotron radiation experiment) M\"ossbauer spectra.