Trapped Atomic Fermi Gases

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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.