  In a recent paper entitled "High temperature expansion applied to fermions
near Feshbach resonance" (Phys. Rev. Lett. 92, 160404 (2004)), Ho and Muller
have demonstrated a remarkable similarity between its high and low temperature
properties at resonance. The quantum second virial coefficient plays a crucial
role in their analysis, and has a universal value at resonance. In this paper,
we explore the connection between the quantum and classical second virial
coefficients, and show that near a Feshbach resonance, an exact mapping from
the quantum to classical form is possible. This gives rise to a scale
independent inverse square potential for the classical second virial
coefficient. It is suggested that it may be tested by measuring the isothermal
compressibility of the gas on the repulsive side of the resonance.
