  We consider a dilute gas of neutral unpolarized fermionic atoms at zero
temperature.The atoms interact via a short range (tunable) attractive
interaction. We demonstrate analytically a curious property of the gas at
unitarity. Namely, the correlation energy of the gas, evaluated by second order
perturbation theory, has the same density dependence as the first order
exchange energy, and the two almost exactly cancel each other at Feshbach
resonance irrespective of the shape of the potential, provided $(\mu r_s) >>
1$. Here $(\mu)^{-1}$ is the range of the two-body potential, and $r_s$ is
defined through the number density $n=3/(4\pi r_s^3)$. The implications of this
result for universality is discussed.
