Dirac neutrino scatterings and nuclear matter effects in supernova core

We consider in detail the production of right-handed neutrinos via helicity-flipping weak-interaction scatterings of neutrinos in the supernova core. We point out the frame dependence of the helicity-flipping scattering cross sections, and present a numerical study of the cross sections in the center-of-mass and laboratory frames. We also discuss briefly the many-body corrections to the scatterings. In particular, we find that for degenerate neutrinos-nucleon scattering rate is reduced to be comparable to the neutrino-lepton one. (orig.)