Charged current neutrino interactions in hot and dense matter

TL;DR

This paper derives relativistic charged current neutrino absorption rates in dense matter, incorporating nuclear mean field shifts and weak magnetism, providing accurate formulas and an open source implementation for astrophysical simulations.

Contribution

It presents a comprehensive derivation of neutrino absorption rates including previously neglected response components, applicable at arbitrary degeneracy and density.

Findings

Response components previously omitted are significant at high density.

Derived formulas are valid for arbitrary matter degeneracy.

Open source implementation available for supernova and neutron star merger simulations.

Abstract

We derive the charged current absorption rate of electron and anti-electron neutrinos in dense matter using a fully relativistic approach valid at arbitrary matter degeneracy. We include mean field energy shifts due to nuclear interactions and the corrections due to weak magnetism. The rates are derived both from the familiar Fermi's Golden Rule, and from the techniques of finite temperature field theory, and shown to be equivalent. In various limits, these results can also be used to calculate neutral current opacities. We find that some pieces of the response have been left out in previous derivations and their contribution at high density can be significant. Useful formulae and detailed derivations are presented and we provide a new open source implementation of these opacities for use in radiation hydrodynamic simulations of core-collapse supernovae and neutron star mergers.