Mössbauer diffraction. III. Emission of Mössbauerγrays from crystals. A. General theory

Abstract

We develop the dynamical theory of the emission of M\"ossbauer $\ensuremath{\gamma}$ rays from crystals. The direct solution of the multiple-scattering equations, valid in the near and far zones, is obtained along with that utilizing the generalized reciprocity theorem. As in the x-ray case, the emission pattern exhibits the Kossel cone structure, but there are interesting new features. Enhanced-intensity "anomalous-emission" Kossel lines are predicted in the early development of a radioactive source as consequence of the fact that the electronic scattering absorption of the lattice is predominantly $E1$, while most M\"ossbauer transitions correspond to the emission of higher-order-multipole waves. In addition, the sensitivity of the M\"ossbauer scattering to the magnetic field and electric-field-gradient tensor at the nucleus gives rise to unique Kossel cones which exhibit the structure of the internal fields. Finally, Faraday effects are important in determining the polarization state of the emitted $\ensuremath{\gamma}$ quanta. Kossel analysis can also be used to determine the phase of the x-ray structure factor of (molecular) crystals. In this paper we develop the general theory describing the optics of M\"ossbauer $\ensuremath{\gamma}$ emission from crystals.