Incoherent ultrarelativistic channeling particle scattering by electrons

The problem of high-energy charged particle motion in the field of atomic strings and planes of oriented crystals, widely applied to control large accelerator beams and generate intense gamma radiation, is addressed. Following the previously developed theory of channeled particles incoherent scattering by crystal atom nuclei, we consider here the same by crystal atom electrons. The theory developed takes into consideration all the effects of momentum transfer between fast particles and electrons of atoms in a crystal in the range from the nuclear radius up to the many inter-atomic distances. The theory also includes the temperature-dependent Debye – Waller factor, as well as both the atomic form factors and scattering function, evaluated with the detail consideration of atomic structure. All the modifications of electron scattering in crystals are reduced to the value of the effective minimum momentum transfer, which by an order of value exceeds that one, related with the Bethe – Bloch mean atomic energy. Substituting this quantity to the expression for the mean square of the scattering angle of a classically moving particle makes it possible to compare the scattering by electrons and nuclei, while its joint use with the Rutherford cross section allows for the correct simulations of the planar channeling of positively charged particles in the thickest crystals, supposed to be used for the beam extraction from high energy accelerators, measurement of electromagnetic characteristics of short-living particles and development of intense narrow-band X-ray and gamma radiation sources based on crystal undulators.