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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?

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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.

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