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Stimulated gamma radiation of free isomer nuclei upon anti-Stokes transitions

The resonance anti-Stokes conversion of broadband X-ray radiation to stimulated gamma radiation of free isomer nuclei is considered. The conversion involves the two-quantum transition from the initial long-lived isomer state of a nucleus via an intermediate level to the final state located below the isomer state. The quantum-mechanical calculation of the cross section for resonance stimulated anti-Stokes scattering involving quanta of the different multipolarity yields the estimate of the gain of stimulated gamma radiation in a nuclear beam with the spectrally local inversion and the estimate of the threshold spectral density of the X-ray pump radiation flux.