Mössbauer medium with a hidden nuclear population inversion and negative absorption of gamma quanta

We consider physical foundations of an eventual experiment aimed at observing stimulated gamma-photon emission of long-lived Mössbauer isomers through selective frequency modulation of gamma-resonances establishing hidden population inversion without exceeding the number of excited nuclei over unexcited ones and without additional pumping. The examples of suitable nuclei and numerical estimates of the parameters are presented.