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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:

11 protons

12 neutrons

11 electrons

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?

James
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The simples case is hydrogen, which consists of a single proton and a single electron. Both are fermions, but the hydrogen atom is a boson. The hydrogen atom has different properties then its components. It's a composite entity, and it makes sense to think of the hydrogen atom as a particle -- although it is not an elementary particle. Personally, I feel it is natural to talk about the hydrogen wave function in atomic physics, and I rarely have to stress that it is a composite particle. At "low energy" the hydrogen atom can be described as a single particle.

The spin-statistics theorem now tells us, that if we take two hydrogen atoms and interchange their position, that we and up with the same wave function. This leads to the "bunching" effect at low temperatures, which is called Bose-Einstein condensation.

NotMe
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