The hyperfine structure of energy levels around the ground state seem to enable Feshbach and be intrinsic to it. Why do we need hyperfine levels?
I.e. why is Feshbach specific to ultracold atoms in ground stae, why would a magnetic field in any gas of atoms not achieve the similar effect of inducing atom-atom coupling?
Thanks in advance,
I think what you are forgetting is that a given Feshbach resonance is between two atoms in a certain scattering channel. This means, in particular, that it only occurs for one partial wave. As far as I know, all observed Feshbach resonances have been either s-wave or p-wave, but presumably they also exist for higher partial waves. Anyway, the point is that for a room-temperature gas atoms interact with many of these partial waves, and the impact of any particular Feshbach resonance would be small.
The threshold energy for a partial wave with angular momentum $l$ goes as $E_{th}(l)\sim A (l(l+1))^{3/2}$, where $A$ depends on the inter-atomic potential and masses and might range from 10 $\mu $K - 1 mK. So, at the K scale and above, it would presumably be difficult to see the effects of any one collision channel. However, I do not know if anyone has tried this experiment, or if it would be feasible with some very careful measurement.
There are probably other considerations too. For example, remember that a typical ultracold atomic gas has something like $10^{-6}$ the density of air, which is important for two-body collisions to dominate the physics.
