Doppler effect in the oscillator radiation process in the medium
  The purpose of this paper is to investigate the radiation process of the charged particle passing through an external periodic field in a dispersive medium. In the optical range of spectrum we will consider two cases: first, the source has not eigenfrequency, and second, the source has eigenfrequency. In the first case, when the Cherenkov radiation occurs, the non-zero eigenfrequency produces a paradox for Doppler effect. It is shown that the absence of the eigenfrequency solves the paradox known in the literature. The question whether the process is normal (i.e. hard photons are being radiated under the small angles) or anomalous depends on the law of the medium dispersion. When the source has an eigenfrequency the Doppler effects can be either normal or anomalous. In the X-ray range of the oscillator radiation spectrum we have two photons radiated under the same angle- soft and hard. In this case the radiation obeys to so-called complicated Doppler effect, i.e. in the soft photon region we have anomalous Doppler effect and in the hard photon region we have normal Doppler effect. 
Lekdar Gevorgian, Valeri Vardanyan
hep-ph physics.acc-ph