Pressure of Bose-Einstein condensate

[SlowThinker]

I was wondering, if cooled sodium or rubidium atoms behave as bosons, can they also occupy the same space?

I tried to google a bit, but as usual, articles throw letters like $\beta$, $s$, $\lambda$, $g$ around without bothering to at least give them a name so I could search deeper. I hope this question can be answered without me becoming an expert on the subject...
In particular, what is the maximum density a BEC can have, in theory (with pressure say 1MPa and temperature 0K), and in practice?

 

[DrDu]

I was wondering, if cooled sodium or rubidium atoms behave as bosons, can they also occupy the same space?

No. After all, they are still made up of electrons being fermions. So they will behave something like hard-core bosons.

 

[DrClaude]

In particular, what is the maximum density a BEC can have, in theory (with pressure say 1MPa and temperature 0K), and in practice?

Atomic BECs are very low density. What is the normal state of alkali atoms at some nK? Solid, of course. So the only way to get a BEC is to work in conditions where the atoms don't simply crystallize as you cool them down, which means that 3-body collisions are to be avoided, which can only be done with dilute gases.