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arXiv:nucl-th/0506042 · Physical Review Letters

Resonant Fermi Gases with a Large Effective Range

A. Schwenk, C. J. Pethick

Published Oct 10, 2005• 165 citations
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Abstract

We calculate the equation of state of a Fermi gas with resonant interactions when the effective range is appreciable. Using an effective field theory for a large scattering length and large effective range, we show how calculations in this regime become tractable. Our results are model independent, and as an application, we study the neutron matter equation of state at low densities of astrophysical interest 0.002 fm(-3) < rho < 0.02 fm(-3), for which the interparticle separation is comparable to the effective range. We compare our simple results with those of conventional many-body calculations.

DOI
10.1103/physrevlett.95.160401

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We calculate the equation of state of a Fermi gas with resonant interactions when the effective range is appreciable. Using an effective field theory for a large scattering length and large effective range, we show how calculations in this regime become tractable. Our results are model independent, and as an application, we study the neutron matter equation of state at low densities of astrophysical interest 0.002 fm(-3) < rho < 0.02 fm(-3), for which the interparticle separation is comparable to the effective range. We compare our simple results with those of conventional many-body calculations.
Dilute Fermi gases with large scattering lengths are intriguing physical systems which are just now becoming accessible in laboratory experiments with cold trapped atoms. Their properties are closely related to those of the dilute neutron‐rich matter which may be present in the surface of neutron stars. Fermi systems with such strong short‐range attractive forces lie between traditional BCS theories with small gaps and those where the fermions are tightly bound into pairs, yielding composite bosons. We discuss the Quantum Monte Carlo methods used to study such systems, and report results for the ground‐state energy, the superfluid gap, and other properties. In particular, we compare results with those of neutron matter at subnuclear densities.
A density-functional theory is proposed for strongly interacting fermions with arbitrary large negative scattering length. The functional has only two parameters that are directly fixed to reproduce the universal properties of unitary gas: the so-called Bertsch parameter ${\ensuremath{\xi}}_{0}$ and a parameter ${\ensuremath{\eta}}_{e}$ related to the possible influence of the effective range re{r}_{e}re​ at infinite scattering length aaa. Using most recent quantum Monte Carlo (QMC) estimates of these two parameters, it is shown that the functional properly reproduces the experimental measurements of interacting Fermi systems not only at unitarity but also away from this limit over a wide range of ${(a{k}_{F})}^{\ensuremath{-}1}$ values. The functional is applied to obtain an expression of Tan's contact parameter including the effect of re{r}_{e}re​. Application is finally made to neutron matter. It is shown that most recent QMC results are well reproduced.
A many-body system of fermion atoms with a model interaction characterized by the scattering length a is considered. We treat both a and the density as parameters assuming that the system can be created artificially in a trap. If a is negative the system becomes strongly correlated at densities ρ ∼ |a | −3, provided the scattering length is the dominant parameter of the problem. It means that we consider |a | to be much bigger than the radius of the interaction or any other relevant parameter of the system. The density ρc1 at which the compressibility vanishes is defined by ρc1 ∼ |a | −3. Thus, a system composed of fermion atoms with the scattering length a → − ∞ is completely unstable at low densities, inevitably collapsing until the repulsive core stops the density growth. As a result, any Fermi system possesses the equilibrium density and energy if the bare particle-particle interaction is sufficiently strong to make a negative and to be the dominant parameter. This behavior can be realized in a trap. Our results show that a low density neutron matter can have the equilibrium density. PACS numbers: 05.30.Fk, 24.10.Cn, 71.10.Ca Key Words: trapped Fermi gases; effective interaction
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We consider interacting Fermi systems close to the unitary regime and compute the corrections to the energy density that are due to a large scattering length and a small effective range. Our approach exploits the universality of the density functional and determines the corrections from the analyical results for the harmonically trapped two-body system. The corrections due to the finite scattering length compare well with the result of Monte Carlo simulations. We also apply our results to symmetric neutron matter.
Experiments with cold Fermi atoms can be tuned to probe strongly-interacting fluids that are very similar to the low-density neutron matter found in the crusts of neutron stars. In contrast to traditional superfluids and superconductors, matter in this regime is very strongly paired, with gaps of the order of the Fermi energy. We compute the T=0T=0T=0 equation of state and pairing gap for cold atoms and low-density neutron matter as a function of the Fermi momentum times the scattering length. Results of quantum Monte Carlo calculations show that the equations of state are very similar. The neutron matter pairing gap at low densities is found to be very large but, except at the smallest densities, significantly suppressed relative to cold atoms because of the finite effective range in the neutron-neutron interaction.