How to think about Coulomb repulsion in a Bose-Einstein condensate of nuclei?

Question

I'm not clear as to how to think about a Bose-Einstein condensate of charged bosons:

Should I think of each particle as a separate wave function with interaction terms based on the electromagnetic force i.e. Coulomb repulsion?

Or should I think of the entire condensate as a quantum system with a single wave function in which it makes no longer sense to speak of relations between individual particles, and where their average electromagnetic potential is distributed across the system as a whole?

Comments

Any quantum system is specified by a single state, irrespective of its constitution. For a Bose-Einstein condensate, the appropriate state is a mixed state (canonical ensemble), described not by a wave function but by a density operator.

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The Coulomb interaction manifests itself in the value of chemical potential $\mu$ in an ensemble with variable number of particles. If there is nothing but the Coulomb repulsion, then such a system of particles is unstable and cannot form any BEC.