Nucleons Superimposed on Each Other?

[Talanum46]

Doesn't the way spin pairs in nuclei imply all nucleons are superimposed on each other? Otherwise spin cannot pair without a modifying constant due to the nucleons occupying different positions. This is since angular momentum does not cancel if particles are not at the same position (L = mvr). Their "r" value would not be the same so their "L" can't cancel.

Edited October 10 by Talanum46

[Talanum46]

One may conceptually realize that a spinning of nucleons off the center of the nucleus would produce a lopsided vibration in the nucleus and thus that "L" would not cancel.

[OceanBreeze]

On 10/10/2024 at 2:28 PM, Talanum46 said:

Doesn't the way spin pairs in nuclei imply all nucleons are superimposed on each other? Otherwise spin cannot pair without a modifying constant due to the nucleons occupying different positions. This is since angular momentum does not cancel if particles are not at the same position (L = mvr). Their "r" value would not be the same so their "L" can't cancel.

The short answer is No, a superposition of fermions is prevented by the Pauli exclusion principle.

A bit longer answer:
The Pauli exclusion principle prevents the nucleons from simultaneously occupying the lowest energy, zero momentum state, and instead the overall ground state is formed by the nucleons occupying distinct states such that the total energy is minimized: they are bunched around the origin of momentum space in a sphere; the Fermi surface is the surface of that sphere.

As for angular momentum, keep in mind we are discussing quantum particles where interactions, in particular, the way particles couple, is determined by isobaric spin. The concept contains the term “spin” because its quantum mechanical description is mathematically similar to that of angular momentum. But unlike angular momentum, it is a dimensionless quantity and is not actually any type of spin.

That’s about as deep as I care/can get in this thread. For a better understanding I recommend you review the Semi-empirical mass formula.

 

[Talanum46]

Then spin pairing must be thought of as happening in an abstract epistemological way and not physically. Otherwise there must be vibration due to lopsided spins.