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We present a comprehensive, quantum mechanical treatment of the spontaneous radiation emitted by a relativistic charged particle traversing a crystal in the systematic reflections geometry. Unlike previous models, this one includes the full three-dimensional periodicity of the crystal potential and is valid for all regimes of particle motion. The emission frequencies are shown to be determined by a combination of two mechanisms: momentum transfer to the lattice and interband or intraband transitions in the potential that is perpendicular to the plane of the channel. Those frequencies that rely on momentum transfer are determined by the period of the potential either in the atomic planes that define the channel or perpendicular to them. Both mechanisms are shown to be important in describing the spectrum of the emitted radiation.
Gershon Kurizki andJ. K. McIver
"A Unified Theory Of Radiation From Relativistic Charged Particles In Crystals", Proc. SPIE 0453, Free-Electron Generators of Coherent Radiation, (16 February 1984); https://doi.org/10.1117/12.947127
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Gershon Kurizki, J. K. McIver, "A Unified Theory Of Radiation From Relativistic Charged Particles In Crystals," Proc. SPIE 0453, Free-Electron Generators of Coherent Radiation, (16 February 1984); https://doi.org/10.1117/12.947127