Quantum mechanical approach to planar positron channeling in a hypersonic field (I)

The solutions of the Dirac equation for a positron channeled in a single cr ystal which is excited by a longitudinal hypersonic wave have been obtained for the energy interval of 10 MeV < E less than or equal to 100 MeV, and t he resonance condition for the interaction between hypersound and positron was deduced. It is shown that the total intensity of the channeling radiati on emitted by the relativistic positron in the hypersonic field is formed b y the partial. intensities of several dominating radiative transitions for which the appropriate conservation law and the Doppler shift of the photon frequency have been determined. Owing to the hypersound the transverse ener gy of the positron may increase which leads to a larger bandwidth of the em itted lines.