Abstract
In the framework of quantum electrodynamics the theory of a new type of X-ray radiation emitted by relativistic electrons at channeling conditions is developed beyond the dipole approximation. This radiation takes place when the electron is reflected by or crossed the crystal surface which coincides with one of the crystallographic planes. It is shown that in this case one reveals two kinds of radiation: channeling radiation by reflected particles and diffracted channeling radiation by passed particles. The radiation can be applied for investigation of the crystal surface.
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