# Stern-Gerlach experiment with Bosons

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.

• S-G experiment works only with neutral atoms and the apparatus uses magnetic field to provide deflection. So the incoming particles should posses a magnetic moment that is solely due to the spin of the electron in it.
– UKH
Apr 22, 2016 at 12:07
• Thanks for your answer :) By the way, when it's used with particles like gluons, or excitons, for example, what would happen? What distribution of particles would we have? Apr 22, 2016 at 12:17
• Apr 22, 2016 at 16:01
• Yes, I Ve seen that link yesterday, but it says it hasn t been performed with bosons. What I don t understand,is what could happen if we were able to take these bosons, with the same way we did for electrons,where would they distribute? Apr 22, 2016 at 20:29

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): 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

• Thanks :) And what about the other two positions of the spin? Would they be at a position different from that of the electron case, given that the spin is not h/2 or -h/2 but h, 0 and -h? Apr 23, 2016 at 17:55
• @DomenicoBagnato yes, they would be closer to the centre than in the case of electrons. The magnetic force on the $W$ is equal than the force on the $e^-$, but as the $W$ are heavier, these get less deflected than the electrons. Apr 23, 2016 at 18:01
• When, as I can imagine, particles with integer spin would get a bigger deflection, according to the same principle. Thank you , and happy weekend! :) Apr 23, 2016 at 18:13
• @DomenicoBagnato whoops there is a mistake in my comment above: the magnetic force on the $W$ is twice as large as than on the electrons, not equal. But $m_W\gg m_e$, so the acceleration of the $W$ is way lower than the acceleration of the electrons. If $W$'s and $e$'s had the same mass, the $W$ would get a bigger deflection, but in reality the $W$ are way heavier, and so get less deflected (more inertia). Apr 23, 2016 at 18:17