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Oxygen has 8 protons and 8 neutrons. Based on the nuclear shell model, protons should pair with anti-parallel protons to create singlet spin states, and neutrons should similarly pair with anti-parallel neutrons. So, it seems I should see 4 positive clumps and 4 neutral clumps, and therefore one tetrahedron of protons plus one tetrahedron of neutrons might work.

To be clear, this two-tetrahedron structure is really just a "charge correlation" picture, since any final picture needs to be spherically symmetric (i.e., the final picture has this two-tetrahedron distribution probabilistically "rotated at all angles and translated to all positions" equally). I expect this "crystallization" of internal structure because the residual strong force seems to lock neighboring nucleons at 1fm.

The Coulomb potential pushes the positive charge outwards, so I roughly expect the proton tetrahedron to be bigger than the neutron tetrahedron. Also, from the Coulomb potential (and from the nature of quarks), the +2q charge in each corner of the proton tetrahedron might really be clumpy...and the neutron tetrahedron corners might similarly be clumpy...but my hunch is that the QCD at this low level is still "mostly cloudy" when I'm focusing on the bigger two-tetrahedron structure.

So, here is my crude picture (grey spheres are broader clouds of total charge +2q, green spheres are broader clouds of total charge 0q). Can you improve it? Have I made a mistake by pairing nucleons (should this picture really have 16 clouds instead of 8)?

In case the quarks give further clumpiness, let me say that this picture is for a 1fm-smoothed-charge observable. If you have a good picture with the finer-detailed clumps, including your picture would be the best answer.

(This question about alpha particle structure was helpful in thinking about this.)

Oxygen Nucleus

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    $\begingroup$ Did you read the answers to the linked question? Your model is not very quantum-mechanical. $\endgroup$
    – rob
    Commented Jun 13, 2021 at 1:15
  • $\begingroup$ @rob Yes. It's hard to quickly draw a 3D wave function without resorting to a ball model (but I did say that the balls are really "broader clouds" hoping everyone would realize that this could easily be made into a quantum field charge probability density). $\endgroup$
    – bobuhito
    Commented Jun 13, 2021 at 1:19
  • $\begingroup$ en.wikipedia.org/wiki/Nuclear_shell_model may be helpful. $\endgroup$
    – PM 2Ring
    Commented Jun 13, 2021 at 2:04
  • $\begingroup$ What is the motivation for this? Do you know about isospin? If you randomly pull a nucleon out of 16-O, will it be a proton or a neutron, or, like Schrödinger's cat, will be a mixture of proton (alive) and neutron (dead)??? $\endgroup$
    – JEB
    Commented Jun 13, 2021 at 3:52

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