# Helium 3 atoms as fermions?

Helium atoms are composite particles so a priori their "single-particle" (in this case single atom) state is very complicated. They are nevertheless well-modeled by elementary fermions models like Fermi liquid models or the jellium/electron gas model, depending on temperature. This is intuitively plausible but I have not found a proof in standard textbooks. I mean the hamiltonian of a He gas involves electrons and protons, why can we approximate each He atom, deformed by interactions with the other particles, so neatly as a single particle with very precise properties like antisymmetry for the multi-He state? I guess there are good references. Thanks in advance.

EDIT: I've read that the approximation only holds for tightly bound states. Actually 1 may think about grouping electrons, neutrons and protons in various ways. There would be bosons for our model if we take groups of say 4 e/n/p from different atoms. But these would not be close to He-3 atoms. These would not be close to He-4 atoms either. So we have to take 4n, 2p, 2e to approximate real systems. In any case we should justify approximating He-3 by elementary fermions, and more particularly a fermi gas at high temp, a Fermi liquid at low enough T, or superfluid spin triplet pairs near ground state. This is intuitive if each group of particle is close to a scatering state with equal momenta for 4 n, 2p, 2e. They'd be close to a bound state and since the Hilbert space is the alternativng product of $\infty$-many elementary fermion wavefunctions the scaterring states for those would be close to actual scattering states for a real He atom. Still the fact that all properties of fermions are conserved by real states, justifying the elementary fermion approximation, is not entirely trivial and I'd like to see it carefully worked out somewhere, or explain why it is more trivial than I think. Thanks again.

• Do you think proton is a fermion? If so, why shouldn't we worry about that proton is actually made of quarks there? I think it is the same idea that He3 atom as a whole can be considered as a single fermion, neglecting the internal structure. Because the energy scale in the superfluid problem is too low to resolve the internal structure of He3. – Everett You Dec 5 '15 at 21:29
• Actually the proton is a fermion as much as HE-3. This is a good remark. It's made up of 3 elementary fermions and some gluons. Most protons must look very much alike. Similarly most HE-3 must look very much alike, but not exactly the same. While elementary particles are truly indistinguishable. This is the whole point: how can particles be approximately fermions? Enough so to be modeled as elementary fermions. – plm Dec 13 '15 at 6:19