  Near Feshbach resonances, $n|a|^3\gg 1$, systems of Bose and Fermi particles
become strongly interacting/dense. In this unitary limit both bosons and
fermions have very different properties than in a dilute gas, e.g., the energy
per particle approach a value $\hbar^2n^{2/3}/m$ times an universal many-body
constant. Calculations based upon an approximate Jastrow wave function can
quantitatively describe recent measurements of trapped Bose and Fermi atoms
near Feshbach resonances.
  The pairing gap between attractive fermions also scales as
$\Delta\sim\hbar^2n^{2/3}/m$ near Feshbach resonances and is a large fraction
of the Fermi energy - promising for observing BCS superfluidity in traps.
Pairing undergoes several transitions depending on interaction strength and the
number of particles in the trap and can also be compared to pairing in nuclei.
