Photon-photon interaction in axial channeling

Abstract

We investigate the possibility that high-energy photons are channeled, when passing through an oriented single crystal, due to Delbrück scattering. For this purpose the exact electron propagator for the single-string model is constructed. Starting from a separation of variables, we solve the Dirac equation for a cylindrical electrostatic potential. The propagator for such external fields is constructed from solutions of the radial Dirac equation. This propagator is applied to a calculation of the S matrix for Delbrück scattering. We specify the conditions under which photon channeling takes place. Unfortunately these conditions are only matched for a very small fraction of those photons being produced by channeled electrons.

Channeling and Radiation in Periodically Bent Crystals

“…Consequently, an accurate numerical calculations of the particle dynamics becomes a formidable task [146]. Consequently, an accurate numerical calculations of the particle dynamics becomes a formidable task [146].…”

Supersymmetric structure in the Dirac equation with cylindrically-deformed potentials

“…The wave functions depend parametrically on the quantum number ε (12), which can be continuous or discrete, and |ε| plays the role of a mass for the transverse motion. A particular selection of potentials within the symmetry class III, is relevant to the study of electron channeling in crystals (V S (z) = 0) [11]. A supersymmetric pattern within the present class is obtained for the choice V V (ρ) = α V /ρ and V S (z) arbitrary.…”

“…which commutes with H but anticommutes with R z (11). The operator L connects the doublet states with (n ρ ≥ 1, ±ε) and annihilates the single state with (n ρ = 0, ε > 0).…”

MBN explorer atomistic simulations of 855 MeV electron propagation and radiation emission in oriented silicon bent crystal: theory versus experiment

“…Various approximations have been used to simulate channelling and other related phenomena in oriented crystals. While, formally, most rigorous description can be achieved within the framework of quantum mechanics (see, e.g., [23][24][25][26] and references therein), it has been shown [27] that classical description in terms of particles trajectories provides highly adequate and accurate description in the limit when the number of quantum states N of the transverse motion of a channelling particle is large enough. For light charged particles (electrons and positrons), the strong inequality N 1 becomes well fulfilled for the projectile energy ε in the hundred MeV range and above.…”