Influence of slowing down in the radiator on the Cherenkov radiation angular distributions from relativistic heavy ions at FAIR, SPS and LHC energies

The calculations of Cherenkov radiation (ChR) angular distributions from relativistic heavy ions (RHI) at very high energies (from 30 GeV/u up to 3000 GeV/u) taking into account their slowing-down (ionization energy loss) in a radiator are performed for the first time. The slowing-down of RHI in an optically transparent solid radiator can drastically change the ChR angular distributions at RHI energies of order of 1 GeV/u. The results of calculation show that at higher RHI energies (>30 GeV/u) (FAIR, SPS and LHC), the ChR angular distribution (at the reasonable radiator thickness) is very close to the Tamm-Frank distribution and practically does not depend on the RHI slowing-down in a radiator, if only ionization energy loss is taken into account.