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 $\rho \sim |a|^{-3}$, 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 $\rho_{c1}$ at which the compressibility vanishes is defined by $\rho_{c1}\sim |a|^{-3}$. Thus, a system composed of fermion atoms with the scattering length $a\to -\infty$ 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.