I recently learned in one of my courses that a nucleus could be modeled as a Fermi gas. This led me to think about other fermions and whether or not I could mess around with them as well. Are the binding forces between quarks too strong for us to be able to imagine them as a "non-interacting" gas? Does the mass of the down quark being significantly larger relative to the up quark prevent this from working? I have a basic understanding of quarks so there could be all sorts of reasons why it couldn't work I don't know of, but I would be interested in why this is not (or why this is) possible.
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No, hadrons are decisively different than nuclei. For the Fermi gas model you want weakly interacting fermion constituents.
For a proton, instead, density of states is hardly meaningful: you have zillions of virtual quarks, antiquarks, and gluons (bosons!), barely excluding each other, while the three valence quarks contribute less than 1% to the proton mass. At short distances, they are weakly interacting, by dint of the asymptotic freedom of gluons interactions; but near the hadron radius, of the order of a fermi, the effective interaction strength explodes to infinity. I've never heard about a Fermi gas shortcut for hadron masses.
Cosmas Zachos
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