Cold neutron scattering in imperfect deuterium crystals

The differential cross sections for cold neutron scattering in mosaic deuterium crystals have been calculated for various target temperatures. The theoretical results are compared with the recent experimental data for the neutron wavelengths $\lambda\approx$~1--9~\AA. It is shown that the structures of observed Bragg peaks can be explained by the mosaic spread of about $3^{\circ}$ and contributions from a~limited number of crystal orientations. Such a~crystal structure should be also taken into account in ultracold neutron upscattering due to the coherent phonon annihilation in solid deuterium.