Nuclear Aufbau, and 'orbitals'

[Jess Tauber]

Some time back I'd detailed how the nuclear 'Aufbau' operated, with the formula 2n+l, rather than the n+l we see with the electronic Aufbau. The nuclear version is linked to the fact that for shells, all 'orbitals' must be of the same parity, as opposed to the alternating parity seen in the electronic system.

But unlike the electronic system nobody has ever ascribed 'lobes' to the nucleus, which HAS no central dense core. Rather we see the nucleus as approximating (for most nuclides, anyway) ellipsoids of various stripes. Rare nuclides might have one or more nucleons orbiting the main body, while the individual nucleons IN the main body are supposed largely to remain in the same contact positions with others.

This leads me to wonder now whether the notion of orbit, for nucleons, is less about probabilistic appearance in abstract fuzzy orbitals, and more concrete. If a nucleus rotates, as it must if a deformed ellipsoid, then all nucleons inside it will also describe closed paths, but not necessarily all of the same ones. It is as if they might be tunneling through the main body of the nucleus. This might be thought of as an inversion of what takes place in the electronic cloud. In the latter, electrons never touch, in the former, they must (due to the strong force). But the dance partners keep switching (one partner is as good as any other), though there is a tendency for protons to migrate towards the periphery of the nucleus, due to their mutual repulsion.

I'm also wondering if my hypothesized 'tunneling' effect could be relatable to the 'intruder' phenomenon, where the highest-spin orbital partials from the next-higher shell get stabilized enegetically and are inserted into the structure of the previous shell at points defined by Pascal Triangle combinatorics (specifically doubled triangular numbers of moves from where they *should* be relative to the LS structure of harmonic oscillator shells without spin-orbit effect). Insertion seems like tunneling, at least in part.

Remember also that while the electronic orbitals fill halfway singly before allowing opposed-spin partners within lobe (except for s, which isn't considered a 'lobe'), nucleons pair up IMMEDIATELY upon getting to an even number. Why the difference? In any case, because of this difference, there is no half-filled orbital effect in nuclei. Instead, we see nuclei with even numbers of nucleons more stable overall than those with odd numbers.

Jess Tauber

tetrahed...@gmail.com

[Scott Hutcheon]

Thanks for this,

At 57, I've studied the sciences (primarily information theory, physics, cosmology, and chemistry) for approximately forty years. Well half of that forty years, as the parallel studies have been communications (applied science of), philosophy, history, education, and the arts.

Regarding your discussion on nuclei shapes, as I constantly try to keep up with the evolving research, and in case you haven't seen it: 

https://www.sciencedaily.com/releases/2025/08/250816113512.htm

https://interestingengineering.com/science/watermelon-nucleus-becomes-heaviest-proton-emitter

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[Scott Hutcheon]

Sorry, thought I had attached the paper as well:

On Wednesday, August 20, 2025, Scott Hutcheon <scotth...@gmail.com> wrote:
> Thanks for this,
> At 57, I've studied the sciences (primarily information theory, physics, cosmology, and chemistry) for approximately forty years. Well half of that forty years, as the parallel studies have been communications (applied science of), philosophy, history, education, and the arts.
> Regarding your discussion on nuclei shapes, as I constantly try to keep up with the evolving research, and in case you haven't seen it: 
>
> https://www.sciencedaily.com/releases/2025/08/250816113512.htm
>
> https://interestingengineering.com/science/watermelon-nucleus-becomes-heaviest-proton-emitter
>
>
>
>
>

> <https://ci3.googleusercontent.com/meips/ADKq_NarCKm8FOrsJbO6qCzRlq7NrAdBPOLZf_fGSanoxQuKZbmKkBBI24EfprcIsDsX4jb4LoJkGxhuJ0ZwAYVUbzxaCz3-uKj52_QjAp7NTSXcNUDeb6-0ZJlreCB1Tnv-dn1BotinKdlEH2f4iFf5qxAuVjbLcvQi4zCPzXcP=s0-d-e1-ft#https://s-install.avcdn.net/ipm/preview/icons/icon-envelope-tick-round-orange-animated-no-repeat-v1.gif>Virus-free.www.avast.com

[Jess Tauber]

While news and papers about newly synthesized nuclides can be interesting, in general I'm more into theoretical treatments supported by overwhelming amounts of experimental evidence leading to paradigms accepted by mainstream workers, and draw from such studies to glean new patterns previously unrecognized. That's how I discovered the dependence on Pascal Triangle combinatorics motivating shell sizes and magic numbers in the electronic and nuclear systems, not to mention shell structures in atomic clusters ('superatoms') which share some features with nuclear shell structures. And all these findings were achieved with simple mathematical procedures such as addition, subtraction, multiplication and division.

 From well-known filling sequences. Sometimes all it takes is RECOGNIZING what you're looking at. I've made some pure mathematical discoveries the same way.