The decay of a pure nuclear exciton (immobile collective excitation), created by a pulse of synchrotron radiation, is
analyzed. It is shown that in the later phases of the decay, the exciton becomes localized at the sample's frontal surface.
Inside the sample, the secondary gamma-quanta, emitted by the contracting exciton, are converted into the polaritons
(mobile nuclear excitations), characterized by different frequencies and equal group velocities. On the sample's back
surface, the polariton interference causes a beating structure of the transmitted radiation, observed in experiments.