  We consider a single quantum particle in a spherical box interacting with a
fixed scatterer at the center, to construct a model of a degenerate atomic
Fermi gas close to a Feshbach resonance. One of the key predictions of the
model is the existence of two branches for the macroscopic state of the gas, as
a function of the magnetic field controlling the value of the scattering
length.This model is able to draw a qualitative picture of all the different
features recently observed in a degenerate atomic Fermi gas close to the
resonance, even in the unitary limit.
