Unified approach to structure factors and neutrino processes in nucleon matter

TL;DR

This paper develops a unified theoretical framework using Landau's Fermi liquid theory to accurately calculate neutrino interaction rates in nucleon matter, incorporating many-body effects and modern nuclear interactions.

Contribution

It introduces a comprehensive approach to neutrino processes in nucleon matter that includes mean-field effects and quasiparticle interactions, improving upon previous models.

Findings

Neutrino process rates are reduced compared to one-pion exchange estimates.

The approach accurately models density and spin-density fluctuations in neutron matter.

Modern nuclear interactions and many-body effects significantly impact neutrino process calculations.

Abstract

We present a unified approach to neutrino processes in nucleon matter based on Landau's theory of Fermi liquids that includes one- and two-quasiparticle-quasihole pair states as well as mean-field effects. We show how rates of neutrino processes involving two nucleons may be calculated in terms of the collision integral in the Landau transport equation for quasiparticles. Using a relaxation time approximation, we solve the transport equation for density and spin-density fluctuations and derive a general form for the response functions. We apply our approach to neutral-current processes in neutron matter, where the spin response function is crucial for calculations of neutrino elastic and inelastic scattering, neutrino-pair bremsstrahlung and absorption from strongly-interacting nucleons. We calculate the relaxation rates using modern nuclear interactions and including many-body contributions, and find that rates of neutrino processes are reduced compared with estimates based on the one-pion exchange interaction, which is used in current simulations of core-collapse supernovae.