Response functions of cold neutron matter: density fluctuations

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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.