Solution

[WoutStoffels]

I think the mentioned increase in the energy was derived from an expression which is only valid if the electron cloud is actually *inside* the nucleus. In this case, the positive charges themselves are not present in the origin, so it is not necessary that the energy shift is positive.

[WoutStoffels]

After thinking about it some more and looking at other answers though, I’m not so sure this is enough of an answer. Someone else proposed to me that the system is now no longer electrically neutral, which is not the case for the atom. I think they might be closer to the truth.

[Author]

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