The question is getting at something subtle and not necessarily obvious to me.
It is often claimed that an atom being composed purely of fermions is either a boson or a fermion itself. I interpret this as meaning that the atom can be treated as a fundamental particle (in the sense it can be put into another schrodinger equation without worrying about it's internal structure).
So if for example, I had a box potential, and I put in many fermionic atoms inside it they would have a population described by the Fermi-Dirac distribution, and likewise bosonic atoms would be described by the Bose-Einstein distribution.
- Why is it that composite fermions (i.e., atoms) are not described by either of the two characters (Bosonic, Fermionic)?
This really amounts to saying are atoms fermions or bosons regardless of temperature, spacing, energies, etc. will they always behave in this simple model to any scale? Will they never switch character?
Intuitively, fermions are fermions because they can't overlap. It seems to me that it would be reasonable for them to act different from the fundamental fermions and bosons because the atoms have a nucleus that is localized and an electron distribution that is spread out; so, it would be less probable for the atoms to really be in the same configuration and so truly be indistinguishable. Or put another way, it would be less probable for each fermion to overlap with the corresponding fermion to cause an overall cancellation. But this is an assumption on why composite particles behave so this begs the second question.
- What is the mechanism by which composite particles act like the fundamental constituents they are made of?