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I'm new to this forum and I'm studying semiconductor physics at the moment. I just wanted to ask a thing about the concept of spin: when it was studied for the first time, in the Stern-Gerlach experiment, there was an apparatus that deflected the incident particles with a magnetic field ( the particles had spin 1/2), and those particles were able to locate either in the top or the bottom part of the screen.

My question is: what would happen if in the experiment particles with spin 1, 2, or 3, for example (bosons) were used? Where would the particles accumulate in that case, and why? I know that such an experiment is impossible to do with photons, because they don't posses a magnetical moment, they only posses spin, but I mean in the case of other kind of particles, with integer spin.

Qmechanic
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Domenico Bagnato
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1 Answers1

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Let's say we could perform the experiment with $W^\pm$ bosons. These particles are similar to electrons, but the possible spin states are $-1,0,+1$, that is, three different possibilities. The magnetic moment of these bosons is, therefore, $$ \mu_z=\begin{cases} -\mu_W\\\phantom{+}0\\+\mu_W\end{cases} $$ where $\mu_W=6\ 10^{-6}\ \mu_B$ is the $W$ magneton.

In this case, as there are three different spin states, we would observe three points at the screen instead of two (in general, for particles with spin $S$ we would observe $2S+1$ equidistant points).

The Stern-Gerlach experiment for electrons looks like this (picture taken from Wikipedia):

enter image description here

If we could do the same with $W$ bosons, there would be a third beam, which would be straight, corresponding to the $\mu_z=0$ state.

Some references

AccidentalFourierTransform
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