particle spin (any experimental physicists out there?)

[theMan]

How do/did they actually determine the spins of various elementary particles experimentally? For example, how do they know the spin quantum number of the electron is ±1/2, or that all fermions have half integer spins? How would you determine this experimentally? something with spin magnetic moments perhaps?

I'm just wondering because I've learned a whole lot of physics, but I've never learned how they actually went about finding these things out in real life.

 

[exdeath]

Accelerator detector trajectories of particles caused by their interaction with fields and other particles.

http://en.wikipedia.org/wiki/Stern-Gerlach_experiment

First experimental observation and evidence of spin.

This is the part you're looking for:

If the particle travels through an inhomogeneous magnetic field, then the force on one end of the dipole will be slightly greater than the opposing force on the other end of the dipole. This leads to the particle being deflected in the inhomogeneous magnetic field. The direction in which the particles are deflected is typically called the "z" direction.

If the particles are classical, "spinning" particles, then the distribution of their spin angular momentum vectors is taken to be truly random and each particle would be deflected up or down by a different amount, producing an even distribution on the screen of a detector. Instead, the particles passing through the device are deflected either up or down by a specific amount. (Assuming that the precessing atoms have not had sufficient time to radiate away a significant amount of energy) this can only mean that spin angular momentum is quantized (i.e., it can only take on discrete values). There is not a continuous distribution of possible angular momenta.

 

[theMan]

yes, but how can you determine what the value for spin actually is? for example, lets say you have a bunch of particles, you don't have any idea what they are beyond some basics like their charge. how can you go about determining their value for spin? for example, if you determine the spin of your unknown particle to be ±1/2, it would act very differently than if you measured it to be ±1. So, how could you go about measuring this?

 

[exdeath]

The number/label assigned to spin is based on the total number of discrete projection values and through the requirement that all possible projection paths always differ by a whole number and are symmetric. If you get two total possible discrete projections with your experimental particle, you know has to be either -1/2 or 1/2 (-1/2 and 1/2 differs by 1, a whole number) so the angular momentum can only be 1/2. If you get three discrete projections you know it can be -1, 0, or 1, and the angular momentum is 1, and so on.

There isn't anything to "measure". Spin is just a man made number of discrete self momentum states a particle can take; it's a unit-less number. The difference between, and the way to "measure" and tell apart, a spin 1/2 and spin 1 particle is that the spin 1/2 will show two possible discrete states in the experiment above, while a spin 1 particle shows 3 possible states. That's all it means. Spin is just a abstract way to classify "built in" momentum of a particle that continues to exhibit the property of momentum when the orbital momentum is zero.

Knowing this, for example, if we observed a new undiscovered particle that created 5 possible projection paths in the experiment above, we would say that the particle has a angular momentum, or spin = 2, with the 5 possible projections being -2, -1, 0, 1, and 2. If a total of 4 projection paths were observed, we would classify it as spin = 3/2 with possible values of -3/2, -1/2, 1/2, and 3/2, etc.

http://hyperphysics.phy-astr.gsu.edu/Hbase/quantum/vecmod.html#c1

The numbers don't really have any particular meaning by themselves, except to classify and label the intrinsic behavior of one particle relative to another in human language. In theoretical physics, there is no why or how, it just "is" as we observe, and we assign labels and form a model to classify the results.

 

[theMan]

thanks. that's helpful. but, can you elaborate a little more on why the values must differ by 1? Why can't you have -1/2, 0, 1/2?

 

[theMan]

oh, nevermind, i think i get it. it's because you quantize both the spin angular momentum, and the z-component of angular momentum with integer values.

 

[exdeath]

Found a good discussion on it: http://www.newton.dep.anl.gov/askasci/chem99/chem99297.htm

And http://hyperphysics.phy-astr.gsu.edu/Hbase/quantum/qangm.html

 

[silverpig]

First, spin is not unit-less. When you say something is spin-1/2 you are talking about its quantum number. The actual spin is given by

S = h(bar)Sqrt[s(s+1)]

where S = the spin of the particle and s = the spin quantum number.

Measuring spin directly can be done a number of ways. The first that comes to mind is measuring the energy difference between spin up and spin down states in a known magnetic field by looking at emission/absorption lines.

 

[theMan]

So, i figured it out.... i think. So basically, it's like this:

the spin quantum number s, is assigned as 0, 1/2, 1, 3/2, 2, ....

the magnitude of spin, S, is given by (hbar)(s(s+1))^(1/2)

the z-component of spin is given by (mz)(hbar), where mz can be given by (s, s-1, s-2, ..., -s).

So, for example, if s=1/2, S = (sqrt3)/2(hbar), and Sz = -1/2(hbar) or 1/2(hbar). therefore there are two possible spins, with the same magnitude but a different z-component.

And, if s=1, S = (sqrt2)(hbar) and Sz = -1(hbar), 0, 1(hbar). (3 possibilities.)

So, in theory, if you do a Stern-Gerlach-like experiment (assuming your orbital angular momentum is zero (so all angular momentum is entirely due to spin angular momentum), you can know the spin quantum number s, based on the number of splits, correct?

 

[silverpig]

For the most part yes.

It should be noted that all elementary particles that make up matter are fermions (spin 1/2), and all force carriers (photons, W,Z bozons, gluons) are spin 1 bosons.

Of course protons and neutrons can combine in the nucleus to produces a spin 1 or spin 3/2 nucleus.