Quantum Theory of Channeling Radiation

Abstract

In the MeV region, the density of levels for the transverse motion of channeled electrons and positrons is so low that a quantum description must be applied. After the early papers on channeling radiation, especially by Kumakhov, many different theoretical approaches have been developed.¹ Our treatment² is based on the quantum formalism developed by Lervig et al.,³ and I shall try to show that this approach has important advantages. Through a systematic approximation procedure, a comprehensive and very accurate description can be built up, and the details under discussion are now corrections to photon energies at the 1% level, e.g., a correction from phonon scattering which is analogous to the Lamb shift of atomic levels. Experimentally, line energies can be determined with this precision,⁴ and applications of channeling radiation to study crystal properties such as electron densities⁵.⁶ and thermal vibrations⁷$ depend on the possibility of making theoretical predictions with an accuracy better than 1%.