The annihilation of a neutrino-anti-neutrino pair into photons and the neutrino density in the universe

Abstract

The cross section for the process ν e + ν e → 3γ is calculated in the low-energy approximation, assuming a universal Fermi interaction. It is found that σ≈9.5×10 −60( ω/ m) 10 cm 2 in the c.m. system of the (ν, ν)- pair (ω = E ν + E ν ⪡ m) . If it is assumed that the universe contains degenerate Fermi gases of both neutrinos and anti-neutrinos, the above mentioned process provides the most important way for mutual annihilation of these gases. It results from our calculations that the rate of annihilation of neutrinos and anti-neutrinos is so small for any reasonable Fermi energy of the Fermi gases (smaller than, say, 100 eV), that both degenerate Fermi gases could coexist with negligible annihilation during a time of, e.g., 1.3×10 10y, typical for the present state of the universe.