A general scattering theory of photons (particles) by field targets, periodically depending on time is developed. On the basis of this formalism the scattering of y-quanta is considered by a crystal, which performs enforced vibrations under the influence of alternating fields. The Raman scattering amplitudes and corresponding cross-sections for scattering and absorption of y-quanta by the crystals are calculated. The possibility of compensation of the recoil energy for y-resonance at energies ~2 0 0 keV by infrared lasers is analysed.
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