Symmetric Laue Diffraction of Spherical Neutron Waves in Absorbing Crystals

Well-known Kato's theory of the Laue diffraction of spherical x-ray waves is generalized to the case of the neutron diffraction in strongly absorbing crystals, taking into consideration both the potential and the resonant scattering of neutrons by nuclei. The saddle-point method is applied for estimation of the angular integrals, being more adequate in the case of strongly absorbing crystals than the stationary-phase approximation used by Kato. It is found that the distribution of intensity of diffracted and refracted beams along the basis of the Borrmann triangle strongly depends on the deviation of the neutron energy from the nuclear resonant level.