SHADOWING OF ULTRAHIGH-ENERGY NEUTRINOS

The rise with energy of the neutrino-nucleon cross section implies tha t at energies above few TeV the Earth is becoming opaque to cosmic neu trinos. The neutrinos interact with the nucleons through the weak char ged current, resulting into absorption, and the weak neutral current, which provides a redistribution of the neutrino energy. We Mellin tran sform the neutrino transport equation and find its exact solution in t he moment space. A simple analytical formula is provided, which descri bes accurately the neutrino spectrum, after the neutrinos have travers ed the Earth. The effect of the weak neutral current is most prominent for an initial flat neutrino spectrum and we find that at low energie s (around 1 TeV) the neutrino intensity is even enhanced.