Planar channeled relativistic electrons and positrons in the field of resonant hypersonic wave

The wave function of a planar channeled relativistic particle (electron, positron) in a single crystal excited by longitudinal hypersonic vibrations (HVs) is determined. The obtained expression is valid for periodic (not necessarily harmonic) HV of desired profile and single crystals with an arbitrary periodic continuous potential. A revised formula for the wave number of HV that exerts resonance influence on the state of a channeled particle was deduced to allow for non-linear effects due to the influence of HV.-