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 ${}^1{S}_0$ scattering lengths such as $a_s=-12070fm$ and $+21fm$ are constructed. Such potentials are renormalized with rigorous procedures to give the corresponding $a_s$-equivalent low-momentum potentials $V_{low-k}$, with which the low-momentum particle-particle hole-hole ring diagrams are summed up to all orders, giving the ground state energy $E_0$ of neutron matter for various scattering lengths. At the limit of $a_s\to \pm \infty$, our calculated ratio of $E_0$ to that of the non-interacting 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 $V_{low-k}$ and those with $G$-matrix interactions are compared.

9 pages, 7 figures

References in corpus (8)

• Thermodynamics of the BCS-BEC crossover
• Precision Measurements of Collective Oscillations in the BEC-BCS Crossover
• Epsilon expansion for a Fermi gas at infinite scattering length
• The potential energy of a ${}^{40}$K Fermi gas in the BCS-BEC crossover
• Finite-Temperature Collective Dynamics of a Fermi Gas in the BEC-BCS Crossover
• Magnetic field control of elastic scattering in a cold gas of fermionic lithium atoms
• Thermodynamics of a Trapped Unitary Fermi Gas
• BEC-BCS Crossover in the Epsilon Expansion

Cited by in corpus (2)

• Low-momentum NN interactions and all-order summation of ring diagrams of symmetric nuclear matter
• Low-momentum interactions with Brown-Rho-Ericson scalings and the density dependence of the nuclear symmetry energy