Abstract:
We calculate the transition radiation process $\nu \to \nu \gamma$ at the border of two media with different (photon) index of refractions. The neutrinos are taken to be with only standard-model couplings. The medium fulfills the dual purpose of inducing an effective neutrino-photon vertex and of modifying the photon dispersion relation. We ignore the neutrino masses in the calculations due to their negligible contribution.  The violation of the translational invariance at the direction from one media into another leads to the momentum non conservation at the same direction. We find that the probability of transition radiation is larger by three orders of magnitude (using the medium induced neutrino-photon vertex) than previous calculations (using vacuum induced vertex). The transition probability is about $10^{-18}$ for the electron density typical for neutron star surface.