Laue diffraction of M\"{o}ssbauer and x-ray photons in strongly absorbing crystals

Abstract

The dynamical scattering theory is developed for the Laue diffraction of the M\"{o}ssbauer rays and x-rays, whose angular distribution is comparable with the diffraction angular range. Both the Rayleigh and the resonant nuclear scattering are taken into account. We consider typical case when incident radiation first passes through an entrance slit and afterwards diffracts at the crystal planes within the Borrmann triangle. In calculations of the wave function for $\gamma$-photons, refracted or diffracted in such strongly absorbing crystal, we apply the saddle-point method. The distribution of their intensities over the basis of the Borrmann triangle is analyzed. In the spherical wave approximation of Kato, when aperture of the incident beam much exceeds the diffraction interval, the derived formulae well correlate with the familiar equations of the diffraction theory of X-rays.