Multiple wave scattering formalism and the rigorous evaluation of optical potential for three-dimensional periodic media

Reflection and refraction of neutrons on the surface of a perfectly ordered mono-atomic medium is considered. The method of multiple waves scattering theory is used. An equation for optical potential of a slow neutron interaction with a medium is derived, which permits one to obtain a solution up to any desirable precision. The dependence of the neutron wave-vector inside the perfect crystalline medium on that in the vacuum is discussed. An intimate relation between problems of dynamical diffraction and total reflection at low energies is demonstrated. Some experimentally measurable physical effects are pointed out. The problems of ultracold neutrons in relation to optical potential are reviewed. (author)