2.4: The Uhlenbeck and Goudsmit proposal

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In 1925, Uhlenbeck and Goudsmit postulated the existence of a new intrinsic property of particles that behaved like an angular momentum as a means of explaining these results. This intrinsic property was later termed spin by Pauli, however, the image of a spinning sphere is not likely an accurate one. This new property needs to be viewed as an intrinsic property like mass and charge that is particular to a given type of particle. Note that, unlike mass and charge, there is no classical analog to spin!

As we will see, it was Dirac who later showed that spin arises very naturally in a correct relativistic formulation of the quantum theory. This formulation is embodied in the relativistic generalization of the Schrödinger equation called the Dirac equation. According to the Uhlenbeck and Goudsmit proposal, the spin of a particle should behave like an angular momentum and, therefore, should have an associated magnetic moment

\[{\bf M}_s = {g \mu_{\rm B} \over \hbar}{\bf S}\]

where

\({\bf S}\) is the spin operator.
\(g\) is a constant introduced to produce the best fit with experiment.

The interaction with a magnetic field is proportional to \({\bf M}_s\cdot {\bf B}\), which is the basis of the NMR technique. It is found that good fits to experimental data are obtained when \(g=2\), which means that the spin gyromagnetic ratio, defined to be \(g\mu_{\rm B}/\hbar\) is twice as large as the orbital gyromagnetic ratio \(\mu_{\rm B}/\hbar\).