Quantum Effects for Parametric $X$-ray Radiation during Channeling: Theory and First Experimental Observation

The theory of $x$-ray radiation from relativistic channeled electrons at the Bragg angles – parametric $x$-radiation (PXR) during channeling (PXRC) – is developed while accounting for two quantum effects: the initial population of bound states of transverse motion and the transverse “form-factor” of channeled electrons. An experiment was conducted using a $255$ MeV electron beam from a linac at the SAGA Light Source. We have identified a difference in the angular distributions of PXR and PXRC and obtained a fairly good agreement between the theoretical and experimental results.