Low-momentum ring diagrams of neutron matter at and near the unitary limit

Abstract

We study neutron matter at and near the unitary limit using a low-momentum ring diagram approach. By slightly tuning the meson-exchange CD-Bonn potential, neutron-neutron potentials with various {sup 1}S{sub 0} scattering lengths such as a{sub s}=-12070 fm and +21 fm are constructed. Such potentials are renormalized with rigorous procedures to give the corresponding a{sub s}-equivalent low-momentum potentials V{sub low-k}, with which the low-momentum particle-particle hole-hole ring diagrams are summed up to all orders, giving the ground state energy E{sub 0} of neutron matter for various scattering lengths. At the limit of a{sub s}{yields}{+-}{infinity}, our calculated ratio of E{sub 0} to that of the noninteracting case is found remarkably close to a constant of 0.44 over a wide range of Fermi-momenta. This result reveals an universality that is well consistent with the recent experimental and Monte Carlo computational study on low-density cold Fermi gas at the unitary limit. The overall behavior of this ratio obtained with various scattering lengths is presented and discussed. Ring-diagram results obtained with V{sub low-k} and those with G-matrix interactions are compared.