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Conditions for the appearance of a nuclear exciton in a crystal consisting of excited and unexcited nuclei of a given type are determined. The total probabilities for spontaneous -emission by a single excited nucleus or by an arbitrary number of excited nuclei in the crystal are derived. It is shown that the formation of a nuclear exciton is connected with an increase of the width of the emitting level and with the concentration of the radiation in a narrow solid angle.

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