Neutrinos decoupled from $\beta$-processes and supernova explosion
  Based on the gravitational collapse time-scale is larger than the weak interaction time-scale at core densities $\rho > 10^{11} {gr}/ {cm}^{3}$, we approximately use the $\beta$-equilibrium condition and particle number conservations to calculate the number and energy densities of neutrino sphere in the process of gravitational core collapse towards the formation of a proto-neutron star. We find that at core densities $\rho_{dec} > 10^{12} {gr}/ {cm}^{3}$, the $\beta$-equilibrium condition cannot be satisfied consistently with charge, baryon and lepton number conservations, leading to the presence of excess neutrinos decoupling from the $\beta$-equilibrium. These excess neutrinos interact with nucleons and electrons via the neutral current channel only and their diffusion time is about $10^{-2}$ sec. The excess neutrino flux could play an important role in an Supernova explosion, provided the fraction of excess neutrinos over all neutrinos is at least one present. 
R. Mohammadi, Remo Ruffini and She-Sheng Xue
astro-ph.HE hep-ph