  Cold atom traps and certain neutron star layers may contain fermions with
separation much larger than the range of pair-wise potentials yet much shorter
than the scattering length.
  Such systems can display {\em universal} characteristics independent of the
details of the short range interactions.
  In particular, the energy per particle is a fraction $\xi$ of the Fermi
energy of the free Fermion system.
  Our main result is that for space dimensions D smaller than two and larger
than four a specific extension of this problem readily yields $\xi=1$ for all
$D \le 2$ whereas $\xi$ is rigorously non-positive (and potentially vanishing)
for all $ D \ge 4$. We discuss the D=3 case. A particular unjustified recipe
suggests $\xi=1/2$ in D=3.
