Weak magnetism for antineutrinos in supernovae

Weak magnetism increases antineutrino mean free paths in core collapse supernovae. The parity violating interference between axial and vector currents makes antineutrino-nucleon cross sections smaller then those for neutrinos. We calculate simple, exact correction factors to include recoil and weak magnetism in supernova simulations. Weak magnetism may significantly increase the neutrino energy flux. We calculate, in a diffusion approximation, an increase of order 15% in the total energy flux for temperatures near 10 MeV. This should raise the neutrino luminosity. Weak magnetism also changes the emitted spectrum of $ \bar\nu_x$ (with $x=\mu$ or $\tau$) and $\bar\nu_e$. We estimate that $\bar\nu_x$ will be emitted about 7% hotter than $\nu_x$ because $\bar\nu_x$ have longer mean free paths. Likewise weak magnetism may increase the $\bar\nu_e$ temperature by of order 10%. This increase in temperature coupled with the increase in neutrino luminosity should increase the heating in the low density region outside of the neutrino sphere. This, in turn, could be important for the success of an explosion. It is important to check our results with a full simulation that includes Boltzmann neutrino transport and weak magnetism corrections.