Atomic Nucleus Spin: Theory & Explanation

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Discussion Overview

The discussion revolves around the theoretical basis for the spin of atomic nuclei, focusing on the contributions of individual nucleons and the complexities involved in predicting nuclear spin states. It encompasses aspects of nuclear physics, quantum chromodynamics (QCD), and the mathematical modeling of nuclear interactions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that the total spin of a nucleus is derived from the sum of the angular momentum and spin of individual nucleons, with the structure of energy levels playing a crucial role.
  • One participant challenges the assertion that "pairs always cancel out," citing Vanadium-50 as an example of a nucleus with aligned pairs contributing to its spin.
  • Another participant notes that Vanadium-50 has two unpaired nucleons, supporting the idea of both unpaired protons and neutrons contributing to the total spin.
  • There is a suggestion that the nuclear interaction is more complex than electromagnetic interactions, leading to unusual spin configurations in certain nuclei.
  • Questions arise regarding the relevance of QCD to nuclear spin, with some participants arguing that effective models are more applicable due to the complexity of full QCD analysis for large nuclei.
  • Participants discuss the applicability of the Schrödinger equation to nuclear systems, noting that potential models can vary significantly based on the interactions considered.
  • One participant emphasizes that while QCD may not work perturbatively at nuclear scales, alternative calculation methods like lattice QCD exist.

Areas of Agreement / Disagreement

Participants express differing views on the cancellation of pairs in nucleon spins and the applicability of QCD to nuclear physics. The discussion remains unresolved regarding the best approach to model nuclear spin and the role of QCD.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about nucleon interactions and the complexity of potential models for nuclear systems. The dependence on definitions of terms like "orbital" and "spin" is also noted.

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The value is the sum from the individual nucleons: their angular momentum and their spin.
Both protons and neutrons have energy levels similar to the electrons, but their energy structure is more complicated. Pairs always cancel out, but you can have a single proton or neutron (or both) leading to the total spin. If you know the structure of the energy levels, you can predict the state they are in, and therefore the total spin.
 
I agree with what you say except for "pairs always cancel out". To pick a nucleus at random, Vanadium-50 is spin 6+. Lots of aligned pairs.
 
Vanadium 50 is odd/odd, you have two unpaired nucleons there. That is the "or both" case I mentioned.
 
That gets you to spin-1. It's 6+.

Pierce, to get back to your question, the answer is "yes", but it's not simple. The short answer is that you have shells like you do in atoms, but because of the fact that the nuclear interaction is more complicated than electromagnetism, the order in which the shells fill moves around quite a bit, and you can end up with bizarre situations like 12 of 50 nuclei all spinning in the same direction.
 
Is this kind of stuff studied in QCD?
 
Vanadium 50 said:
That gets you to spin-1. It's 6+.
Doesn't that come from orbital angular momentum? Okay, that's interesting. That would probably require weird energy levels.

@pierce15: QCD is more relevant "inside" hadrons. Nuclear physics uses effective models as a full QCD analysis gets too complex for large nuclei.
 
As mfb said, it's too hard to study a system like V-50 in QCD. It has 150 valence quarks.
 
So do are all the protons and neutrons (or individual quarks) in a nucleus described by orbitals?
 
  • #10
Yes, the nuclei are in orbitals, but predicting these orbitals is harder than it is in chemistry.
 
  • #11
Does the Schrödinger equation then describe the system? If so, what would the potential be for ionized deuterium?
 
  • #12
It's not "hard" to study QCD for nuclear physics... I'd better say it's meaningless... QCD stops working perturbatively at the nucleus range [energies]. So your results are not predicting at all...

Yes the Schrod. equation can describe the system [because the nucleons are not relativistic]. You can look for the potential... it depends on what interactions you allow... eg some standard potential well for the nuclear force, maybe spin-orbit coupling, spin-spin coupling etc... The nuclear potentials in general can be very difficult to be determined, they can contain many terms, some coming from "theoretical" background, others coming straightforward from experiments, and then other experiments are needed to determine your parameters.
 
  • #13
ChrisVer said:
It's not "hard" to study QCD for nuclear physics... I'd better say it's meaningless... QCD stops working perturbatively at the nucleus range [energies]. So your results are not predicting at all...

That would be true if the only way to do a calculation was perturbation theory. But it's not. There's also the lattice.
 

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