We have theoretically shown that the yield of diffuse radiation generated by
relativistic electrons passing random multilayered systems can be increased
when a resonant condition is met. Resonant condition can be satisfied for the
wavelength region representing visible light as well as soft X-rays. The
intensity of diffusive soft X-rays for specific multilayered systems consisting
of two components is compared with the intensity of Cherenkov radiation. For
radiation at photon energy of 99.4eV, the intensity of Resonant Diffusive
Radiation (RDR) generated by 5MeV electrons passing a Be/Si multilayer
exceeds the intensity of Cherenkov radiation by a factor of ≈60 for
electrons with the same energy passing a Si foil. For a photon energy of
453eV and 13MeV electrons passing Be/Ti multilayer generate RDR exceeding
Cherenkov radiation generated by electrons passing a Ti foils by a factor
≈130.Comment: Talk presented at the RC2005, Frascati, Ital