Superfluid Fermi gases and neutron matter with low-momentum interactions
ABSTRACT :
Two-component Fermi gases with an attractive contact interaction can be considered an experimentally accessible toy model for dilute superfluid neutron matter as it exists in the crust of neutron stars. Starting from the idea that many-body effects should not depend o n short-distance or high-momentum physics which is encoded in the s-wave scattering length, but only on momentum scales of the order of the Fermi momentum, we build effective low-momentum interactions that reproduce the scattering phase shifts of the contact interaction below some momentum cutoff. Inspired from recent successes of such methods in nuclear structure theory, we use these interactions to describe the equation of state of the Fermi gas in the framework of Hartree-Fock-Bogliubov theory with perturbative corrections. In the BCS regime, there is a range of cutoffs where we obtain fully converged results. Near unitarity, convergence is not yet reached, but we obtain promising results for the ground-state energies close to the experimental ones [1]. Similarly, dilute neutron matter can be described with low-momentum interactions (called v_{low-k}) including finite-range effects and higher partial waves in addition to the s-wave scattering length. Results for the neutron- matter equation of state obtained in this way will be discussed [2].