Quantum resonances in reflection of relativistic electrons and positrons

Calculations based on the use of realistic potential of the system of crystallographic planes confirm earlier results on existence of resonances in reflection of relativistic electrons and positrons by the crystal surface, if the crystallographic planes are parallel to the surface.The physical reason of predicted phenomena, similar to the band structure of transverse energy levels, is connected with the Bloch form of the wave functions of electrons (positrons) near the crystallographic planes, which appears both in the case of planar channeling of relativistic electrons (positrons) and in reflection by a crystal surface. Calculations show that positions of maxima in reflection of relativistic electrons and positrons by crystal surface specifically depend on the angle of incidence with respect to the crystal surface and relativistic factor of electrons/positrons. These maxima form the Darwin tables similar to that in ultra-cold neutron diffraction.