Small-angle x-ray transition radiation from multilayered structures

In this work, we construct for the first time the theory of small-angle transition radiation from multilayered structures. The theoretically obtained spectral and angular distributions of radiated photons are compared with those predicted by Geant4, a very popular package used today for numerical simulation of different physical processes. We demonstrate that, while spectral distributions ideally coincide, the angular ones differ. We argue that transition radiation from the multilayered structure must contain sharp spikes having the interference nature and caused by the effect of merging two maximum frequencies in dispersive media, and thus Geant4 needs improving in this respect. The transition radiation theory developed here for the small-angle case can play a vital part for the possible future Small Angle Spectrometer at the LHC, other experiments of this kind, and detectors for hadrons of the tera-electron-volt energy range.