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Given a large (say, at least as big as lithium), approximately-spherical atomic nucleus, what does the interior charge distribution look like? I.e., is it relatively uniform, concentrated towards the center, concentrated towards the surface, linear (as in a deuteron), or something else entirely? Is that even something that can be generalized, or is it expected to be significantly different for every nucleus, without trending towards any particular limiting configuration?

Qmechanic
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Logan R. Kearsley
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In most simple models, the same single-particle nuclear potential is used for both neutrons and protons, with the result that the wavefunctions have density profiles that look pretty much alike. The decent success of the flat-bottomed Woods-Saxon potential in reproducing various experimental facts suggests that it is a pretty good approximation to imagine nuclei as having constant density throughout their interiors. This makes sense in terms of the liquid drop model, which in turn makes sense because of the short-range nature of the nuclear force.

In more sophisticated models, such as Hartree-Fock calculations where the single-particle potential is derived in a way that is meant to be approximately consistent with the wavefunctions, you can see effects such as a tendency in heavy nuclei for the protons to spread out a little due to Coulomb repulsion. In some extremely helium-rich nuclei (stuff like $^{10}\text{He}$), you can get a very extensive "skin" of weakly bound neutrons.

Experimentally, proton charge distributions are easier to probe than neutron charge distributions, with techniques such as electron scattering. Some experiments (e.g., atomic physics measurements) are sensitive to quantities such as the charge quadrupole moment. IIRC you can see profiles in some cases like the bottom of a wine bottle, and there can be variation between nuclei due to shell effects. E.g., an orbital with high angular momentum will tend to have its probability distribution more concentrated toward the outside.

linear (as in a deuteron)

I doubt that the charge distribution in a deuteron is at all linear. The proton is in a spatial "s" orbital, which is spherically symmetric.

  • I was basing my assumption about the deuteron on https://physics.stackexchange.com/questions/273724/what-is-the-shape-of-a-deuterium-nucleus, which seems to indicate that the charge is concentrated towards the ends. It is entirely possible that I have misinterpreted that wrt charge distribution, though. – Logan R. Kearsley Jan 28 '18 at 02:36
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    @Logan, it is dangerous to interpret un-explained visualizations. I chased links from 273724 in search of a clear statement of what the visualization means, and the best I found was from https://www.jlab.org/highlights/archive/phys.html (about half-way down the page): "The tensor moment $t_{20}$ is most sensitive to the deuteron's charge distribution, while the other two moments, $t_{21}$ and $t_{22}$, provide important symmetry checks and information about the deuteron's magnetization. The shapes associated with these moments are shown" which might or might not imply it shows charge. – dmckee --- ex-moderator kitten Jan 28 '18 at 03:41
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    @LoganR.Kearsley: Both the mass and the charge distribution in the deuteron are very nearly uniform and spherical. The deviation from spherical shape is about 5% (long/short). –  Jan 28 '18 at 16:31
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In the approximation of extended nuclear matter (which is pretty good for $A > 40$) the charge distribution is constant in the bulk and rolls off smoothly but fairly abruptly around the edges. I think the scale for that roll off is about $1\,\mathrm{fm}$, but my copy of Walecka is at the office.

dmckee --- ex-moderator kitten
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  • It's not constant in the bulk, from electronic scattering we know that the charge distribution has a denser "skin" toward the edge due to repulsive interactions, see ie http://physics.gu.se/~f3aamp/tl.pdf – AwkwardWhale Oct 19 '23 at 11:54