Kinematical theory of Moessbauer diffraction by magnetically ordered crystals

The kinematical theory of Moessbauer diffraction by magnetically ordered crystals is developed. The case of completely resolved Zeeman splitting of a Moessbauer line is examined in detail. The expressions for coherent scattering amplitudes and scattering cross sections of γ-rays at magnetic and crystalline diffraction maxima are derived for the main types of magnetic ordering (ferromagnetic, antiferromagnetic, weak ferromagnetic and helicoidal structures) in the case of the dipole Moessbauer transition. A direct connexion between the polarization of the scattered quanta and the magnetic and crystalline structure is revealed in the expression obtained for polarization vector and the polarization density matrix (in the cases of polarized and unpolarized incident beams respectively). The explicit form of the polarization density matrix at magnetic reflexions for an antiferromagnet is given. The applications of the present results to experimental and theoretical investigations are discussed. (Auth.)