Raman scattering of a photon with frequency doubling by a channelled positron

We have analysed the possibility of appearance of anti-Stokes lines in the spectrum of Raman scattering of a photon by a 'quasi-bound' charged particle in the regime of planar (axial) channelling. It is shown that radiation may emerge at the frequency, which is a combination of the incident photon frequency ω₀ and transition frequency ω_i in the transverse quantised motion of a channelled particle: ω = ω₀ ± 2γ²ω_i, where γ is the relativistic (Lorentz) factor of a channelled particle.