Planar channeling radiation in the presence of a hypersonic superlattice

The radiation emitted by a relativistic electron/positron planar channeled in a single crystal and simultaneously swinging transversely due to longitudinal hypersonic (HS) vibrations excited in the crystal has been investigated. In the present case, the continuum potential of crystallographic planes has been obtained by averaging the corresponding atomic potentials over an area, the size of which was chosen to be much smaller than the wavelength of the quasi-stationary HS field. The spatially periodic HS superlattice involves a zone structure of the channeling states. Probabilities of radiant transitions as well as spectral-angular distributions of the intensity of the corresponding channeling radiation have been calculated assuming parametric resonance. Numerical results are given for several crystallographic planes of -quartz.