Response functions of cold neutron matter: Density fluctuations

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/pF, where pF is the Fermi momentum. The leading order O(q2) 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(q4). 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 q2 scaling for the pair-breaking neutrino emission from neutron stars is discussed.