Theory of polarimetric resonance electron Mössbauer spectroscopy

Abstract A general expression is derived for the shape of a 57 Fe resonance electron Mossbauer spectrum due to a multilayer sample with arbitrarily polarized incident γ-radiation. The coefficients of the spherical tensor expansions of the density matrices of the eigenstates of the general hyperfine Hamiltonians of the nuclear excited and ground states are first calculated in terms of the hyperfine parameters referred to an arbitrary coordinate system. The coefficients are given explicitly both for pure magnetic hyperfine interaction and for pure electric quadrupole interaction in the excited state. The absorption matrices for the different transitions are then calculated in terms of these coefficients and the direction of propagation of the incident radiation. The general shape of the spectrum involves the traces of the multiple-order products of the absorption matrices and the density matrices of the incident radiation. The shape function also depends on the thicknesses of the layers and on the attenuation coefficients of the different kinds of radiation. A number of computed spectra is presented, and examples of experimental spectra fitted to the appropriate theoretical shapes are discussed. Values of the hyperfine angular parameters are directly obtained from the fits.