# Bose-Einstein Condensate bonding

How would a material bond with a BEC? Would it have valence electrons? If you were to have a couple hundred atoms in BEC, would they bond with a couple hundred other atoms, a lower amount that how many atoms, or just one? How does that works?

BEC usually have very low densities ("dilute"), with $$\sim 10^{13}$$ particles cm$$^{-3}$$ vs $$\sim 10^{22}$$ particles cm$$^{-3}$$ for a usual solid.
This is because BEC atoms do bond, they form molecules. A solid is the real ground state of the material, a BEC is just a metastable state that decays to a solid by creating molecules via three-body recombination events. These involve 3 atoms, so as to conserve momentum and energy, otherwise not-allowed in 2 atom processes of identical particles, and go as $$a^4 n^3$$, where $$n$$ is the density and $$a$$ the scattering length (quantifying the scattering length).
So low densities $$n$$ are needed to even have a metastable BEC in a lab. Denser (more $$n$$) and more interacting (more $$a$$) bond more quickly and form a solid faster.