Quantum-Mechanical Approach to Planar Positron Channeling in a Longitudinal Hypersonic Field

The wave function of a planar-channeled positron with energy
10 MeV£E£100 MeV
under the resonant influence of hypersound is calculated.
It is found that the longitudinal hypersound changes the spectral
distribution of the channeling radiation significantly.
With decreasing wavelength l _s of the hypersound,
starting from l _s=l _E,
where l _E is the characteristic
length related to one transverse oscillation of the channeled positron,
a new type of radiative transition occurs.
It is characterized by the stimulated enhancement of transverse
energy of the positron at channeling (inverse radiative transition).
When l _s approaches l _E/2 the inverse
transitions show a resonant behaviour.