# Stern Gerlach and Nuclear Spin?

1. Mar 27, 2015

So, my current understanding of spin is that when particles with a certain spin state hit a stern gerlach device, their wavefunction is split into components, deflection associated with one of the pure spin states aligned with the device. For spin 1/2 particles, there are only supposed to be two beams.

For large composite particles like silver atoms though: shouldn't the spin of the nuclear particles also contribute to the composite particle's spin state? (And neutrons do apparently have a magnetic moment, so they should react to the magnetic field). (I see silver is about evenly split between silver-107 and silver-109 (both with odd numbers of nucleons)).

If you were to run something like cadmium (with a much broader spread of isotopes) through a Stern gerlach device, wouldn't you have to get some sort of even/odd isotopic separation effect? I cannot think of any reason why a magnetic field acting on an atom should only act on the electrons!

This bugs me, because there is a very clear isotopic separation effect for something like the superfluidity of helium. Helium 3 behaves differently than helium 4.

Last edited: Mar 27, 2015
2. Mar 27, 2015

### Staff: Mentor

You have to consider the strength of the interaction. For electrons, it is of the order of the Bohr magneton $\mu_B$, while for nuclei the nuclear magneton is approximately
$$\mu_N \approx \mu_B \frac{m_e}{m_p}$$
You would need a very strong magnetic field to separate atoms according to their nuclear spin.

3. Mar 27, 2015

Thank you. I'll have to look at this more closely.

To restate: The rate of the deflection then is proportional to the magnetic moment of the particle being acted on. Neutrons have the same spin as electrons (composite of 3 spin-1/2 quarks) but due to having higher mass have a lower magnetic moment. In the Stern-Gerlach example, if you could resolve the bifurcated smudge further (by a factor of 1800), would you see further fine splitting due to nuclear spin?

Actually, that just spawns further questions:
Has anyone taken a proton before and put it into a different spin state (spin 3/2, say? All quarks in same spin direction. I imagine it would be a higher internal energy state.)

For that matter, has anyone attempted to do something to increase the angular momentum state of a fundamental particle - say, put an electron into a spin 3/2 state by doing something like suddenly changing a strong magnetic field? (No clear ideas on how to attempt doing this yet, and I can't imagine it would be easy.)

The orbital angular momentum of a particle is adjustable by changing the particle's mechanical situation (higher energy levels have higher angular momentum states available.) It would be interesting to see if there is any internal structure to intrinsic particle spin, and if what we think of as the fundamental spin of particle X is just a ground state of sorts.

Last edited: Mar 27, 2015
4. Feb 10, 2016

### drvrm

The Stern–Gerlach experiment strongly influenced later developments in modern physics:

• In the decade that followed, scientists showed using similar techniques, that the nuclei of some atoms also have quantized angular momentum. It is the interaction of this nuclear angular momentum with the spin of the electron that is responsible for the hyperfine structure of the spectroscopic lines.
• In the 1930s, using an extended version of the Stern–Gerlach apparatus, Isidor Rabi and colleagues showed that by using a varying magnetic field, one can force the magnetic momentum to go from one state to the other. The series of experiments culminated in 1937 when they discovered that state transitions could be induced using time varying fields or RF fields. The so-called Rabi oscillation is the working mechanism for the Magnetic Resonance Imaging equipment found in hospitals.
• Norman F. Ramsey later modified the Rabi apparatus to increase the interaction time with the field. The extreme sensitivity due to the frequency of the radiation makes this very useful for keeping accurate time, and it is still used today in atomic clocks.
• In the early sixties, Ramsey and Daniel Kleppner used a Stern–Gerlach system to produce a beam of polarized hydrogen as the source of energy for the hydrogen Maser, which is still one of the most popular atomic clocks.
• The direct observation of the spin is the most direct evidence of quantization in quantum mechanics.
• The Stern–Gerlach experiment has become a paradigm of quantum measurement. In particular, it has been assumed to satisfy von Neumann projection. According to more recent insights, based on a quantum mechanical description of the influence of the inhomogeneous magnetic field,[12] this can be true only in an approximate sense. Von Neumann projection can be rigorously satisfied only if the magnetic field is homogeneous. Hence, von Neumann projection is even incompatible with a proper functioning of the Stern–Gerlach device as an instrument for measuring spin.
• for details see <https://en.wikipedia.org/wiki/Stern–Gerlach_experiment#Importance>