Quantum theory of X-ray radiation at Bragg angles at channeling

• For the first time we developed theory of the DCR beyond the dipole approximation.
• The applicability of the dipole approximation is considered.
• Analytically shown that DCR angular distribution represents system of double rings.
• In planar case angular distribution is not symmetrical with respect to X- and Y-axis.

In the framework of quantum electrodynamics the theory of the new type of X-ray radiation from the channeled electrons in vicinity of the Bragg angle—Diffracted Channeling Radiation (DCR) is developed beyond the dipole approximation. The DCR occurs due to transitions of the channeled electrons from one transverse energy level to another with the diffraction of the emitted photon. It is demonstrated that dipole approximation is valid for the first order of diffraction DCR and not valid for higher orders of diffraction. On the basis of obtained equations for the first time it is theoretically shown that the angular distribution of the DCR is a system of very narrow ring-shaped peaks around of the Bragg direction. The calculations were performed taking into account the band structure of the transverse motion energy.