Fine structure of the Vavilov–Cherenkov radiation

Abstract

We found relativistic quantum corrections to the one-photon Cherenkov emission. It is proved that, in the absence of dispersion, the Vavilov–Cherenkov radiation fills the whole Cherenkov cone (in the Tamm–Frank theory the Vavilov–Cherenkov radiation for the fixed refractive index is confined to the surface of the Cherenkov cone). The radiation intensity reaches the maximum inside the Cherenkov cone. It turns out that photons with different energies fly at different angles in the interval from zero up to the Cherenkov angle corresponding to the initial charge velocity. The visible light region, where the Vavilov–Cherenkov radiation is usually observed, is surrounded by the low intensity infrared region and by the high intensity one corresponding to high energy photons. The ratio of the radiation intensity at the maximum lying in the Roentgen part of the radiation spectrum to the radiation intensity in its visible part is about 10 4 . Taking into account the medium dispersion leads to the appearance of the striped-like radiation structure inside the Cherenkov cone. Experimental data indicating the existence of a non-zero radiation field inside this cone are discussed. In the past, non-relativistic quantum corrections to the radiation intensity were found by Ginzburg. Yet, he did not analyse their influence for large energy–momentum transfer.