Quantum theory of the dynamical Čerenkov emission of x rays
Abstract
X-ray photons propagating in a crystal close to the Bragg-diffraction directions have an effective index of refraction that may be larger than 1. Electrons moving rapidly in crystals may therefore emit x rays. This process, the dynamical \ifmmode \check{C}\else \v{C}\fi{}erenkov radiation (DCR) of x rays, is studied with use of a theory that is closely analogous to the quantum theory of the \ifmmode \check{C}\else \v{C}\fi{}erenkov effect in homogeneous media. Features of the DCR process that are calculated include the spectral width due to x-ray absorption, the systematic deviations of the photon energy from Bragg's law, the influence of the orientation of the crystal surface, etc. Extensions of the theory to cover many-beam diffraction cases or more detailed calculations of the small recoil effects are straightforward to carry out. The photons are emitted at the far tails of the diffraction region, they are overwhelmingly in the ``diffracted'' plane-wave component, and, in the two-beam case there is no anomalous Borrmann absorption. DCR is a particularly efficient emission process for hard x rays (several tens of keV) with extremely high spectral density (within small angular regions). The emission rate is highest at the energy \ensuremath{\Elzxh}\ensuremath{\omega}=\ensuremath{\gamma}\ensuremath{\Elzxh}${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$ (${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$ is the plasma frequency), but, because of absorption, the number of photons…
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