Particle Spin: Exploring Coulombic Repulsion & Spin Correlation

[eagleone]

Particle spin has always been one of my favorite physics topics. You could always find the question to ask the teacher or later professor and not get the answer (starting with the simplest “what is it” :), “why is it”, “why some particles have it, some not”, “why does it give rise to magnetic momentum, how” ... etc (I may forgot some more interesting, there’s always later)).

But, I have more specific one’s. We all know that electrons occupy different orbitals of a given subshell before dubly occupying anyone of them. In that way they manage to have the same spins, spins are in the parallel arrangement. Explanation is lowering Coulombic repulsion between electrons. Why is that, I know that probability of finding two electrons with parallel spins in same orbital is 0, but how that helps this lowering of Coulombic replulsion, and net lowering of enrgy ? Than this effect of spin correlation leads to shrinking of atom slightly, and improving nucleus –electron interaction. If that’s so, what’s with the proton – electron spin interaction (correct me if I’m wrong they both have 1/2 spin), then should I conclude that in this case better orientation would be antiparallel one ?

 

[Ambitwistor]

Hmm, it's been some time since I've looked at spin-spin interactions in atoms... this page goes into slightly more detail:

http://hyperphysics.phy-astr.gsu.edu/hbase/atomic/atstruct.html#c2

 

[futz]

Roughly, you can think of it like this: Pauli Exclusion says that 2 electrons cannot share the exact same quantum state. So, electrons with parallel spins don't like each other much, and will tend to push each other apart. As the distance between them increases, the Coulomb energy decreases, resulting in a lower energy state for the atom.

More technically, electrons are fermions, which require an antisymmetric wave function. A parallel spin configuration is symmetric, requiring an antisymmetric spatial wavefunction, which in general means the electrons will be farther apart (once again, reducing the total energy).

This is the basis of Hund's 1st Rule.

 

[volantis]

Originally posted by eagleone
But, I have more specific one’s. We all know that electrons occupy different orbitals of a given subshell before dubly occupying anyone of them. In that way they manage to have the same spins, spins are in the parallel arrangement. Explanation is lowering Coulombic repulsion between electrons. Why is that, I know that probability of finding two electrons with parallel spins in same orbital is 0, but how that helps this lowering of Coulombic replulsion, and net lowering of enrgy ? Than this effect of spin correlation leads to shrinking of atom slightly, and improving nucleus –electron interaction. If that’s so, what’s with the proton – electron spin interaction (correct me if I’m wrong they both have 1/2 spin), then should I conclude that in this case better orientation would be antiparallel one ?

First of all, I don't think spin refers to the actual rotation of the subatomic particle. I say this based on my recent analysis of nucleus spin. It appears that spin is a function of space that is imparted to the subatomic particle.

The arrangement of nuclear spin was researched by Linus Pauling and his spheron model seems to be the best fit for spin arrangement in the nucleus. I have further expanded Linus Pauling's work and arranged the nuclear spin into a chart that shows the pattern of spin development.

(I'm working on a new view of physics based on the strong nuclear charge as opposed to mass, energy, or momentum.) Scan to the bottom of this page to see the charts...
http://www.tshankha.com/detailed_atomic_structure.htm

There appears to be something else about a subatomic particle that determines whether it is "parallel" or "antiparallel" as you call it.

As for the spin of the electron, you might get some more insights from an electron binding energy equation for the ls orbitals that I've been working on...
http://www.tshankha.com/electron_binding_energies.htm

This equation incorporates spin into calculating the binding energy of the electron's ls orbital for any atom from lithium to uranium within about 5% accuracy. The equation is obviously not complete, but it may give some insight into the nature of spin. And like in the nucleus example I gave above, this equation suggests spin is a characteristic of the spacetime the electron occupies with respect to the atom it is attached to, not a literal spinning motion.

Dave

 

[Loren Booda]

futz seems basically correct. Ambitwistor provides a helpful diagram.