Mixed optical Cherenkov-Bremsstrahlung radiation in vicinity of the Cherenkov cone from relativistic heavy ions: Unusual dependence of the angular distribution width on the radiator thickness

The Cherenkov radiation (ChR) angular distribution is usually described by the Tamm-Frank (TF) theory, which assumes that relativistic charged particle moves uniformly and rectilinearly in the optically transparent radiator. According to the TF theory, the full width at half maximum (FWHM) of the ChR angular distribution inversely depends on the radiator thickness. In the case of relativistic heavy ions (RHI) a slowing-down in the radiator may sufficiently change the angular distribution of optical radiation in vicinity of the Cherenkov cone, since there appears a mixed ChR-Bremsstrahlung radiation. As a result, there occurs a drastic transformation of the FWHM of optical radiation angular distribution in dependence on the radiator thickness: from inversely proportional (TF theory) to the linearly proportional one. In our paper we present the first analysis of this transformation taking account of the gradual velocity decrease of RHI penetrating through a radiator.