  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 as well as a realistic angular dispersion of
incident neutrons. The saddle-point method is applied for estimation of the
angular integrals, being more adequate in the case of strongly absorbing
crystals than the usually used stationary-phase approximation. It is found that
the intensity distribution of the diffracted and refracted beams along the
basis of the Borrmann triangle significantly depends on the deviation of the
neutron energy from the nuclear resonant level. When comparing our calculations
with the Shull's experimental data on neutron diffraction in silicon we regard
also the role of finite width of the collimating and scanning slits.
