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Protons inside, electrons outside. But why not the other way around?

Every time I try to understand how forces which hold atoms and molecules together work, I find myself wanting to ask this question: why not the other way around? Could there be an atom which has electrons and neutrons inside, and protons outside?

It feels like a silly question, but is there something we know about the universe we live in that implies that this is not possible?

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  • Electrons are not subject to the strong nuclear force that glues the protons neutrons together. This means that no attractive force would prevent electric repulsion to scatter a "electron nucleus".

    From a field theory perspective, the strong nuclear force is a SU(3) gauge interaction and the electron field transforms as a singlet under that SU(3)

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