Pump and amplification dynamics of gamma rays in a nuclear medium with the hidden population inversion

The features of the pump dynamics of isomeric nuclei excited by X-rays of a repetitively pulsed relativistic electron beam followed by the production of a medium with the negative absorption of gamma quanta are analysed. In the extended nuclear medium, the pump excites a travelling hidden-population-inversion wave with the anisotropic gamma amplification, which becomes positive in the case of the excess over the critical pump parameter equal to the product of the peak spectral power density of the X-ray source and the relative duration of an ultrashort relativistic electron bunch. In the alternative scheme with orthogonal directions of pumping X-rays and a flux of amplified gamma quanta, the absence of the amplification anisotropy opens up the possibility for constructing a standard two-mirror resonator with Bragg single-crystal reflectors. The critical peak value of the spectral pump power density is compared with the known characteristics of relativistic-electron X-ray sources by examples of some nuclides.