On the problem of the unthresholdness of Vavilov-Cherenkov radiation (X)

Abstract

Angular distributions of radiation occuring at the passing of particles of different velocities through transparent media of different thickness have been calculated in this paper on the basis of various formulae for the intensity of the Vavilov-Cherenkov radiation (VChR) and the optical transitional radiation. In all cases, i.e. at particle velocities both above and below the VChR threshold, the angular distributions are represented as sets of maxima of different orders of K. For particle velocities above the VChR threshold there are maxima with both positive and negative K in addition to the zero (Cherenkov) maximum ( K = 0). At velocities below the VChR threshold there are only maxima with positive K in the angular distributions. Comparison of the angular distributions of the radiation calculated by Tamm's formulae (for radiation within the medium) and by Pafomov's formulae (for radiation outside the medium) with the angular distributions of the transitional radiation described by the Ginsburg-Frank formulae has shown that the radiation at velocities below the VChR threshold is also transitional radiation, though not a continuous one (as in the case of particles crossing the boundary of semi-infinite media) but with maxima of different orders. This “transformed” transitional radiation accounts for the unthresholdness effect earlier found by Kobzev and Frank.