As asked in How is a Bose-Einstein condensate produced from sodium atoms that do not have an integer spin? , Sodium 23 has been used experimentally to form a Bose Einstein condensate.
Sodium 23 is the only naturally occurring sodium isotope. Its components are:
Since fermion pairings are only possible for even number of fermions presumably of the same type, I don't understand how the odd 1 proton and odd 1 electron can be reduced, such that all fermions are paired, which is a necessary condition for the measurements taken on the lump to reflect Bose Einstein statistics?
I don't fully understand the answer given in the ref: "Sodium-23 has nuclear spin of 3/2, making it a fermion. There are 12 paired neutrons, 10 paired protons, and one leftover unpaired proton. The unpaired proton sits in a shell state which contributes the spin of 3/2. But the Bose-Einstein condensate is formed by atomic sodium, not nuclear sodium. The 11 electrons in a neutral sodium atom contribute an unpaired spin of 1/2 to the total. The full sodium atom is a composite boson, so it can form a Bose-Einstein condensate."
What has happened to the odd 1 proton and odd 1 electron which has enabled all present fermions to reduce to bosons in this lump of matter?