Abstract
Approximate solutions of the Dirac equation are found for ultrarelativistic particles moving in a periodic potential, which depends only on one coordinate, transverse to the largest component of the momentum of the incoming particle. As an example we employ these solutions to calculate the radiation emission of positrons and electrons trapped in the planar potential found between the (110) planes in Silicon. This allows us to compare with the semi-classical method of Baier, Katkov and Strakhovenko, which includes the effect of spin and photon recoil, but neglects the quantization of the transverse motion. For high-energy electrons, the high-energy part of the angularly integrated photon energy spectrum calculated with the found wave functions differs from the corresponding one calculated with the semi-classical method. However, for lower particle energies it is found that the angularly integrated emission energy spectra obtained via the semi-classical method is in fairly good agreement with the full quantum calculation except that the positions of the harmonic peaks in photon energy and the photon emission angles are shifted.
Highlights
Under certain circumstances, when a high-energy charged particle enters a crystalline medium, the particle dynamics is not dominated by the scattering on single atoms but rather by the coherent scattering on many atoms, resulting in a smooth, bound motion along crystal axes or planes [1]
Channeling radiation from high-energy electrons/positrons represents one of the few experimental realizations of nonperturbative and nonlinear problems in quantum electrodynamics, where the field strength experienced by the particle in its rest frame approaches the Schwinger field Ecr 1⁄4 1.3 × 1016 V=cm, see Fig. 1
We present an investigation of planar channeling, based on wave functions that are approximate solutions of the Dirac equation in the realistic Doyle-Turner model of the periodic crystal potential and calculate the single-photon radiation emission without any of the mentioned approximations
Summary
Under certain circumstances, when a high-energy charged particle enters a crystalline medium, the particle dynamics is not dominated by the scattering on single atoms but rather by the coherent scattering on many atoms, resulting in a smooth, bound motion along crystal axes or planes [1]. This motion leads to radiation emission called channeling radiation. Channeling radiation from high-energy electrons/positrons represents one of the few experimental realizations of nonperturbative and nonlinear problems in quantum electrodynamics, where the field strength experienced by the particle in its rest frame approaches the Schwinger field Ecr 1⁄4 1.3 × 1016 V=cm, see Fig. 1.
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