Thermalization:To test this, we have developed an algorithm for solving the full collision term of the neutrino Boltzmann equation in an isotropic homogeneous thermal bath of scatterers. We set the temperature, density, and composition of the bath to reflect representative points at snapshots in time within a corecollapse supernova. To the right we include a movie showing equilibration via both scattering processes and a figure, which summarizes the thermalization rate. 


Production:In order to test the validity of this approximation, we study production of mu and tau neutrinos in a isotropic thermal bath. Given zero initial phasespace occupancy at all energies, we solve the Boltzmann equation for the time evolution of the neutrino phasespace distribution function using the full production integral. We follow both neutrinos and antineutrinos. The final equilibrium phasespace distribution should be FermiDirac with zero chemical potential. To the right we include a movie showing production of the equilibrium Fermi sea of neutrinos via both bremsstrahlung and electron/positron annihilation. We also include a figure summarizing the relevant rates at two different points in a representative stellar profile. 


NucleonNucleon Bremsstrahlung:To the right are two figures that illustrate the difference between the nondegenerate limit, which generally overpredicts the rate, and the case of arbitrary degeneracy. 

