We compare Newtonian three-flavor multigroup Boltzmann (MGBT) and (Bruenns) multigroup flux-limited diffusion (MGFLD) neutrino transport in postbounce core collapse supernova environments. We focus our study on quantities central to the postbounce neutrino heating mechanism for reviving the stalled shock. Stationary-state three-flavor neutrino distributions are developed in thermally and hydrodynamically frozen time slices obtained from core collapse and bounce simulations that implement Lagrangian hydrodynamics and MGFLD neutrino transport. Most important, we find, for a region above the gain radius, net heating rates for MGBT that are as much as ~2 times the corresponding MGFLD rates, and net cooling rates below the gain radius that are typically ~0.8 times the MGFLD rates. These differences stem from differences in the neutrino luminosities and mean inverse flux factors, which can be as much as 11% and 24%, respectively. They are greatest at earlier postbounce times for a given progenitor mass and, for a given postbounce time, greater for greater progenitor mass. We discuss the ramifications these new results have for the supernova mechanism.
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