The production of gamma-ray Cherenkov-transition radiation (GCTR) by charged
particles in the photon energy region 0.8 - 2 MeV is studied theoretically
using the results of the recent discovery that in the above mentioned region
the dielectric constant or the refraction index of some materials is greater
than 1 due to Delbruck scattering on Coulomb field of nuclei. Using the results
of the carried out numerical calculations, the possibility of observing GCTR
and some of its applications are discussed
