The continuous transition from quantum channeling to the Bragg diffraction at the constant energy

Abstract

It is well known that diffraction effects belong to the low-energy realm of wave physics, while the channeling effect resides in the high-energy realm of particle physics. The energy increase induces the transition between these two effects and is a well-understood singular semiclassical limiting process.In this paper, it will be shown that in the case of high-energy electron diffraction, the change of beam angular divergence can induce a continuous transition between the quantum planar channeling of electrons and Bragg's electron diffraction at the constant energy. In the described settings, the appearance of the diffraction maxima in the angular distribution of the transmitted electrons will be connected with the appearance of the quasi-stationary quai-periodic waves in crystal channels.