Channeling Radiation in Strained Layer Super lattices — A Quantum Mechanical Calculation

Abstract

When energetic charged particles are injected along a high symmetry crystal direction, then because of the ordered structure of the target atoms, such a particle will undergo a correlated series of small angle gentle collisions, leading to a phenomenon known as channeling. The idea that the oscillatory motion of these channelons should lead to emission of radiation has been discussed from the very beginning, on the basis of classical electrodynamics. In quantum mechanical framework, the longitudinal motion is considered to be nearly free particle type whereas the transverse motion is bounded by the atomic planes (or axes). This confined motion results in the formation of the discrete bound states in the transverse continuum potential. The transitions among these transverse energy levels lead to radiative phenomenon called Channeling Radiation. These transitions are analogous to spontaneous decay of excited states in atomic physics. However since the oscillatory frequencies (ω) are low, the corresponding energies are of the order of a few eV only, the observation of the radiation seemed to be difficult. The realization that relativistic effects will shift the photon energy into keV or even MeV region was a turning point. In the rest frame the relativistic motion results in Lorentz contraction along the axes or plane and hence the strength of the continuum potential is enhanced by a factor γ(where γ=1/√(1- v²/c²)).