Collective Behavior of the Closed-Shell Fermi Gas

We propose an unconventional description for the ground state and collective oscillations of the two-component normal Fermi gas with two-body zero-range interactions. The many-body problem can be accurately reduced to a linear, one-dimensional Schroedinger equation in a single collective coordinate, the hyperradius R of the N-atom system which is the root mean square radius. The calculated properties of the Fermi gas ground state are shown to agree accurately with results from the Hartree-Fock (HF) approximation over a wide range of interspecies scattering lengths. The breathing mode excitation frequency deviates qualitatively from HF predictions, but we show that this reflects a failure of the HF approach for this observable.