  The spectrum of electromagnetic waves emitted by an oscillator trapped in an
external potential well is studied. It is assumed that the natural frequency of
the oscillator is much greater than the frequency of oscillations in the
potential well. We consider the quantum model of emission with regard to the
recoil effect. The highest intensity of the absorption and emission lines is
observed on the natural frequency of the oscillator when the recoil energy is
equal to the energy of the quantum of low-frequency (LF) oscillations in the
potential well.
  A certain decrease in the amplitude of the emission and absorption lines is
noted caused by the oscillations of the potential well due to, for example, the
presence of the phonon spectrum. The relaxation times of the oscillator LF
motion in the potential well, resulted from the phonon emission, are estimated.
It is concluded that these processes have no influence on the observed features
of the emission and absorption of high-frequency photons. This model can be
applied to description of the emission and absorption of gamma rays in the
crystal structures even in the presence of the phonon spectrum on condition
that the relaxation time of the LF movements in the potential well is greater
than the lifetime of the HF oscillator.
