Channeling Radiation

Abstract

In the early studies of electron and positron channeling^1,2, the interest was focussed on the relation to the diffraction phenomena observed in the electron microscope. Could the electron be treated as a localised classical particle, as in the theory of channeling³, or should it rather be considered an extended wave, scattering coherently off crystal planes, as in the theory of electron diffraction⁴? After much controversy, a clear picture emerged: The answer depends on the magnitude of the electron energy E=γmc². At low energies, i.e., for γ≈1, diffraction effects are very important, and the channeling behaviour is determined by the properties of a few bound states in the axial or planar continuum potential. However, since the effective mass in the transverse motion is the relativistic mass γm, the number of bound states increases with increasing electron energy, and a classical description is approached⁵. In fact, since the effective mass can be varied continuously, channeling has provided a beautiful textbook illustration of the gradual transition towards a classical picture in the limit of large quantum numbers (correspondence).