  A new mechanism of electromagnetic radiation by electrons under the influence
of a dense neutrino flux, termed "the spin light of electron" in neutrino flux
($SLe_\nu$), is considered. It is shown that in the case when electrons are
moving against the neutrino flux with relativistic energy there is a reasonable
increase of the efficiency of the energy transfer from the neutrino flux to the
electromagnetic radiation by the $SLe_\nu$ mechanism. The proposed radiation
process is applied to an astrophysical environment with characteristics
peculiar to supernovae. It is shown that a reasonable portion of energy of the
neutrino flux can be transferred by the $SLe_\nu$ to gamma-rays .
