Can The Free Electrons Be Polarized?

[wantommy]

Recently, I read the Stern-Gerlach experiment
and I have a question about the source

use free electrons beam instead of Ag atoms beam
is the screen still two lines (electron spin up & down)?

But the truth is that there is a region(pattern) not two obvious lines on the screen
because the electrons can't be polarized in the S-G equipment
I'm just curious that
how to calculate it to prove there isn't two lines on the screen?

Can any gurus derive it and show me?
Thank you!

there is a information which i found
jstor search "27757542"
(A History of the Question: Can Free Electrons be Polarized?)
but the context doesn't have the derivation@@ (just interpret the history...)


best regards

 

[Morgoth]

I don't understand your question.
As you have small magnetic dipole momenta (does it come from the angular mommentum or the spin) passing through a mangetic field (S-G) they will get polarised. What does that mena?
That generally means, that initially your magnetic dipole momenta were showing in every direction, let us say chaotically.
After getting in the field, they will get their momenta get to that magnetic field lines' direction (so either UP or DOWN). It's classical...

 

[wantommy]

Here is the context :
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In 1808, Malus found that the light can be polarized by sending it through a calcite crystal. In 1921, Stern and Gerlach found that when they sent an atomic beam (for example, alkali atomic beam) through an inhomogenious magnetic field, then detected the polarization of atoms. For example, the alkali atomic beam splits into two beams with opposite spin directions. In the former case, a calcite crystal is the so-called "polarizer", and the latter case a "spin filter".
However, the procedure does not work with free electrons! Namely, it is impossible to polarized free electrons by means of a Stern-Gerlach experiment. That is to say, when you send an electron beam through an inhomogeneous magnetic field, no splitting with opposite spin directions can be observed.
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Thus
I think "be polarized" that lead the atomic beam split to two state (Beacuse of angular momentum L&J)

My question is
if I change atomic beam into free electron beam
how can I show that Stern-Gerlach apparatus cannot separate spin-up and spin-down electrons?

thanks for your response!

 

[Morgoth]

http://galileo.phys.virginia.edu/classes/252/Angular_Momentum/Angular_Momentum.html
Here says that with Hydrogen (l=0) it worked just fine.
I don't know where you found that info, yet I don't understand why it would not.
I mean OK, if you want to avoid coulomb forces between them, you can send them 1-1 through the S-G.

 

[wantommy]

The info is that my teacher gives to me & let me think about it
he just imply that I need the "Lorentz force and uncertainty principle"

maybe the atomic beam is electrically neutral and don't consider Lorentz force
but the free electron beam has charge not electrically neutral, it should use the Lorentz force to fix it

my teacher asks me to convince him how should I "calculate" it fo fix the problem in S-G apparatus...

I searched lots of webs and found nothing clues about fixed derivation
is my keyword wrong@@?

Sincere best wishes

 

[Meir Achuz]

Electrons can be polarized, but not by the S-G apparatus.
The problem there is that the spread in deflection due to the -evXB interaction for an inhomgeneous B is about the same as the grad(mu.B) deflection, so discrete beam separation is not seen for charged paarticles.