A Generalized Kompaneets Formalism for Inelastic Neutrino-Nucleon Scattering in Supernova Simulations

Understand

Based on the Kompaneets approximation, we develop a robust methodology to calculate spectral redistribution via inelastic neutrino-nucleon scattering in the context of core-collapse supernova simulations.

• The resulting equations conserve lepton number to machine precision and scale linearly, not quadratically, with number of energy groups.
• The formalism also provides an elegant means to derive the rate of energy transfer to matter which, as it must, automatically goes to zero when the neutrino radiation field is in thermal equilibrium.
• Furthermore, we derive the next-higher-order in {\epsilon}/mc2 correction to the neutrino Kompaneets equation.