Calculation of Positron Channeling Radiation with a Harmonic Potential
  We present a detailed calculation of channeling radiation of planar-channeled positrons from crystal targets in the framework of our approach, which was proposed recently. In contrast to previous calculations of channeling radiation in crystals, our calculation takes into account the interference between different transition amplitudes. The development stemmed from the idea that the amplitude for a given process is the sum of the transition amplitudes for each transition to lower state of transverse energy with the same energy differences between bound-bound transitions. It seems that a consistent interpretation is only possible if positrons move in a nearly harmonic planar potential with equidistant energy levels. 
V.F.Boldyshev, M.G.Shatnev