Fresnel coefficients for parametric X-ray (Cherenkov) radiation

Parametric X-ray (Cherenkov) radiation (PXR) is considered to result from the crystal diffraction of virtual photons associated with a relativistic charged particle moving through the crystal. Formulas for PXR Fresnel coefficients are obtained in a kinematic approach, whose applicability is discussed. The derivation of the version of kinematic PXR theory using the Fresnel coefficients is described. By also using these coefficients, analytical expressions for the frequency, spectral peak width, differential yield by angles, and polarization of PXR are obtained and shown to compare well with the kinematic PXR theory of Ter-Mikaelian and with experimental PXR reflection studies.