Influence of Bragg diffraction on perfect crystal neutron phase shifters and the exact solution of the two-beam case in the dynamical diffraction theory

The phase shift of neutrons passing through a sample is usually determined by the sample's index of refraction based on the coherent neutron scattering length. If the sample has a perfect crystal structure there are, however, additional phase effects due to Bragg diffraction. While Bragg peaks in the diffracted direction are very sharp on the angular scale, the phase of the transmitted beam is influenced on a much wider angular range in the order of degrees around the Bragg condition. The magnitude of this effect is in the order of 10^-4 of the refractive phase and clearly visible in interferometry measurements on a perfect silicon sample. In order to calculate the effect, the exact solution is derived for the two-beam case of the dynamical diffraction theory for arbitrary Bragg-plane orientation and arbitrary deviations from the Bragg condition. Even far off any Bragg condition, a residual phase correction remains which is identified as a local field correction.