Response functions of cold neutron matter: density fluctuations

TL;DR

This paper calculates the density response function of cold neutron matter at finite temperature, revealing universal and nonperturbative contributions relevant for understanding neutrino emission in neutron stars.

Contribution

It provides a new effective theory expansion for the response function, including universal leading order and nonperturbative scattering effects.

Findings

Universal q^2 dependence of the response function

Nonperturbative scattering contribution evaluated numerically

Implications for pair-breaking neutrino emission in neutron stars

Abstract

We compute the finite temperature density response function of nonrelativistic cold fermions with an isotropic condensate. The pair-breaking contribution to the response function is evaluated in the limit of small three-momentum transfers q within an effective theory which exploits series expansion in powers of small q/p_F, where p_F is the Fermi momentum. The leading order O(q^2) contribution is universal and depends only on two fundamental scales, the Fermi energy and the pairing gap. The particle-hole Landau Fermi-liquid interaction contributes first at the next-to-leading-order O(q^4). The scattering contribution to the polarization tensor is nonperturbative (in the above sense) and is evaluated numerically. The spectral functions of density fluctuations are constructed and the relevance of the q^2 scaling for the pair-breaking neutrino emission from neutron stars is discussed.