It is usually said that the Pauli exclusion principle is the big arbiter of how particles will distribute themselves along energy levels (especially electrons on atomic orbitals), but how accurate is this statement?
It's rather easy to see for an abstract atom, floating in the void in an empty universe. But the distribution is still roughly the same, as far as I know, if an atom is just far enough from other potentials (for instance, in a gas rather than a solid).
But despite that, technically any perturbation coming from whatever distance should be able to split energy levels, as minutely as that may be.
If the Pauli exclusion principle was the sole arbiter of this, shouldn't then most electrons distribute themselves near the ground state, at very close levels due to perturbations at infinity? I assume that the reason for the absence of such a phenomenon is the interaction between the electrons themselves, is this correct?