# Why nuclear spins \>1?
**URL:** https://boards.straightdope.com/t/why-nuclear-spins-1/976263
**Category:** Factual Questions
**Created:** [December 9, 2022, 3:38pm UTC](https://boards.straightdope.com/t/why-nuclear-spins-1/976263 "2022-12-09T15:38:11Z")
**Posts on this page:** 11
**Page:** 1
### Author:  [@Ruken](https://boards.straightdope.com/u/Ruken)
#### Post date: [December 9, 2022, 3:38pm UTC](https://boards.straightdope.com/t/why-nuclear-spins-1/976263/1 "2022-12-09T15:38:11Z")
My rudimentary\* understanding is that like nucleons can pair and cancel each others’ spin, which is why even-even nuclei are spin 0. I get why the various isotopes have the spins they do until we get to lithium-7, which seems like it could could have a pair of protons, two pairs of neutrons, with an extra proton to yield spin 1/2. But it’s 3/2. Why? I’m assuming there are reasons nucleons don’t pair, perhaps analogous to why electrons don’t always pair?
\*I’m coming at this as an organic chemist typically more concerned about what the electrons are doing, while only occasionally thinking about nuclei when poking them with radio pulses in big magnets. So not quite explain-it-like-I’m-five territory.
---
### Author:  [@DPRK](https://boards.straightdope.com/u/DPRK)
#### Post date: [December 9, 2022, 5:44pm UTC](https://boards.straightdope.com/t/why-nuclear-spins-1/976263/2 "2022-12-09T17:44:38Z")
I guess the energy level of the proton in the second nuclear shell with spin 3/2 is just lower?
[ ](https://upload.wikimedia.org/wikipedia/commons/e/e5/Shells.png)
Wikipedia says
> At all levels, the highest _j_ states have their energies shifted downwards, especially for high _n_ (where the highest _j_ is high). This is both due to the negative spin–orbit interaction energy and to the reduction in energy resulting from deforming the potential to a more realistic one.
---
### Author:  [@Ruken](https://boards.straightdope.com/u/Ruken)
#### Post date: [December 9, 2022, 6:55pm UTC](https://boards.straightdope.com/t/why-nuclear-spins-1/976263/3 "2022-12-09T18:55:13Z")
Ah I see there’s a nuclear shell model I need to read about. I’ll get on that.
---
### Author:  [@DPRK](https://boards.straightdope.com/u/DPRK)
#### Post date: [December 10, 2022, 12:25am UTC](https://boards.straightdope.com/t/why-nuclear-spins-1/976263/4 "2022-12-10T00:25:35Z")
btw, in the nuclear shell model the protons and neutrons _do_ pair as to cancel out their spins, so it is the unpaired nucleon that will determine the angular momentum and parity of the whole nucleus. (And the negative spin-orbit interaction energy makes, for a given _l_ and _s_ = ½, the state with _j_ = _l_ + ½ always have lower energy than the state with _j_ = _l_ - ½.)
For Lithium-7, I looked online and the spin-1/2 state has an energy of 477.6 keV and decays to the ground state by emitting a gamma ray, with half-life of 73 fs.
---
### Author:  [@md-2000](https://boards.straightdope.com/u/md-2000)
#### Post date: [December 11, 2022, 5:18am UTC](https://boards.straightdope.com/t/why-nuclear-spins-1/976263/5 "2022-12-11T05:18:45Z")
As I understand, I only know very basic nucleon stuff, “spin” is just a name. Nucleons don’t actually spin like a top (as far as anyone can tell) what is happening is that they have a form of polarity that can cancel out if two nucleons of opposite poles connect. Spin is just a way of saying how they are polarized…
Same thing, electrons don’t “orbit” the nucleus like a satellite around the earth. they are spread out in a statistical probability “cloud”, and if two electrons occupy the same cloud, it’s because one has an opposite “spin” to the other.
Similarly, quarks aren’t colors. that was another such shorthand to describe a 3-way characteristic that explains their behaviour.
---
### Author:  [@wolfpup](https://boards.straightdope.com/u/wolfpup)
#### Post date: [December 11, 2022, 6:00am UTC](https://boards.straightdope.com/t/why-nuclear-spins-1/976263/6 "2022-12-11T06:00:18Z")
> [@md-2000](#):
>
> As I understand, I only know very basic nucleon stuff, “spin” is just a name. Nucleons don’t actually spin like a top (as far as anyone can tell) what is happening is that they have a form of polarity that can cancel out if two nucleons of opposite poles connect. Spin is just a way of saying how they are polarized…
My very limited understanding – and I welcome any correction – is that although the spin of subatomic particles is not like the spin of a macroscopic object like a top, it’s not a total abstraction, either, because it represents real angular momentum. The bizarre aspects are things like electrons of spin 1/2 having to rotate twice to return to their original state.
---
### Author:  [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)
#### Post date: [December 11, 2022, 8:46am UTC](https://boards.straightdope.com/t/why-nuclear-spins-1/976263/7 "2022-12-11T08:46:16Z")
The physics of nuclear magnetic resonance and derivation of the Larmor frequency can be done with a classical view of spinning bits.
That has always been something that struck me as really underlying the weird nature of quantum spin
---
### Author:  [@DPRK](https://boards.straightdope.com/u/DPRK)
#### Post date: [December 11, 2022, 11:17am UTC](https://boards.straightdope.com/t/why-nuclear-spins-1/976263/8 "2022-12-11T11:17:00Z")
I am not sure the right word is “polarized”, but angular momentum is _quantized._ If the states of the particle form a representation of SU(2) ≅ Spin(3), let’s say an irreducible representation, then the spin is (half of) the highest weight. For a spin-1/2 particle like an electron, the representation is 2-dimensional, so we might say it is polarized. However, consider, for example, _two_ protons. They couple together; the 4-dimensional space splits as a direct sum of a spin-0 representation and also a a spin-1 representation, the latter having _three_ dimensions. Perhaps we can think of there being two “poles” corresponding to the maximum and minimum values of the component of angular momentum along some axis? But it can also take on intermediate values; e.g. 4 possible values for a spin-3/2 particle.
---
### Author:  [@Ruken](https://boards.straightdope.com/u/Ruken)
#### Post date: [December 11, 2022, 12:16pm UTC](https://boards.straightdope.com/t/why-nuclear-spins-1/976263/9 "2022-12-11T12:16:54Z")
None of this is in question, just why certain arrangements end up lower energy than others.
---
### Author:  [@Chronos](https://boards.straightdope.com/u/Chronos)
#### Post date: [December 11, 2022, 1:37pm UTC](https://boards.straightdope.com/t/why-nuclear-spins-1/976263/10 "2022-12-11T13:37:46Z")
And a full explanation of that would require a full understanding of the strong interaction. Which nobody yet has.
We have some approximations of limited validity, and heuristics, and estimates, but nothing like even a full formula.
---
### Author:  [@Ruken](https://boards.straightdope.com/u/Ruken)
#### Post date: [December 12, 2022, 2:53pm UTC](https://boards.straightdope.com/t/why-nuclear-spins-1/976263/11 "2022-12-12T14:53:40Z")
> [@Chronos](#):
>
> And a full explanation of that would require a full understanding of the strong interaction. Which nobody yet has.
So it seems. @DPRK ‘s posts (thank you!) sent me down the wiki-hole and I see how there are parallels with atomic orbitals but the potentials are phenomenologically derived and the force has a tensor component on top of being a function of spin and isospin.