Raman scattering of photons by the channeling electrons

The motion of channeling particles in the accompanying coordinate system can be considered as a two-dimensional atom in the case of axial channeling. The transversal motion of the channeling particles is characterized by discrete spectrum. The occupation probability of the transversal motion levels depends on the entrance angle of the charged particles relative to the crystallographic axis. In the scattering of a photon by the “quasi-bound” electron moving in the axial channeling regime would appear the frequencies ω which are a combination of the incident photon frequency ω0 and the frequency ωNM (ωNM is the transition frequency in transverse quantized motion of the channeling electron: ω=ω0±ωMN, where ℏωMN=2γ2ΔE⊥NM for the relativistic electron, γ2=E/(mc2) is the Lorentz factor of the channeling electron). In the article are discussed the criteria for choosing an adequate continuous potential of the crystallographic axis and the quantum characteristics of a transversal motion of the channeling electron. The peculiarities of the Raman scattering spectrum of photons by electrons in the axial channeling regime are analyzed and the differential cross section of this process is found.