# How is a Bose-Einstein condensate produced from sodium atoms that do not have an integer spin?

In 1995 Wolfgang Ketterle at MIT produced a Bose-Einstein Condensate in a gas of sodium-23 atoms, but sodium-23 doesn't have an integer spin. How does this work?

The protons, neutrons, and electrons that make up any atom are all Fermions with spin $$1/2$$. You can't make a Bose-Einstein condensate out of just electrons, for instance. But a composite particle can have a net integer spin.
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.