Calculation of the Cherenkov light yield of high-energetic particle cascades in IceCube

Cherenkov light occurs if a charged particle in a dielectric moves faster than the phase velocity of light. The radiation emitted by a single track per unit path length and unit frequency of light is given by the well-known Frank-Tamm formula. This formula assumes single particle tracks that are much longer than the emitted wavelength and the size of the polarization region. We will present a first principle calculation of the Cherenkov light yield which is applicable for the case of very high particle densities where the polarization regions of the tracks may overlap. This can be relevant for the recently observed ultra-high-energetic neutrino interactions in IceCube.