Trapped Atomic Fermi Gases

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 ρ c1 at which the compressibility vanishes is defined by ρ c1 ∼ |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. Although a theory of Fermi gases is not yet well developed, there are nevertheless new challenging experimental possibilities to explore trapped Fermi gases [1]. These are expected to stimulate a proper theoretical description of these Fermi quantum systems. Currently this description of quantum Fermi gases at their different states, which can be equilibrium, quasi-equilibrium or far from equilibrium, is usually based on tedious numerical calculations, particularly when the interaction between particles, or atoms, of a gas cannot be considered as weak. This implies that the dimensionless effective coupling constant of the interaction p F a ≥ 1. Here p F is the Fermi momentum and is related to the system's density by ρ = p 3 F /3π 2 , while a is the scattering length. There are a few cases, when it is possible to treat the properties analytically. The Random Phase Approximation (RPA) is applicable for a high density electron gas [2] and the low density approximation deals with dilute gases [3]. In both cases the kinetic energy T k is assumed to be much bigger than the interaction energy E int of the system. This permits the application of some kind of a perturbation theory. In the case of an electron liquid it turns out that the analytical RPA-like …