Coherence and Polarization Effects in Mössbauer Absorption by Single Crystals

Abstract

The polarization dependence of the absorption cross section must generally be taken into account in calculating Mössbauer absorption spectra of single crystals which exhibit hyperfine splittings. A method for doing this in an experimentally interesting class of cases is described. In these cases, the incident radiation beam can be divided into two components, each having its own complex index of refraction. A number of conditions under which this division is always possible are described in terms of crystal symmetry considerations. Also, a practical method of computing the polarization of the cross section in terms of the hyperfine interactions for arbitrary nuclear transitions is described. A representation of the polarization in terms of a 2×2 density matrix is introduced which is convenient in cases where two or more nuclear transitions overlap in energy and in cases where resonant nuclei are located at several different or crystallographically equivalent but differently oriented sites in the crystal. A method for applying these results to an analysis of data to obtain electric-field-gradient parameters, mean square displacements, and magnetic structures is outlined.