The experimental discovery of the internal angular momentum ↩

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aliases: [The experimental discovery of the spin]
created: 2022-01-06 08:10:33
modified: 2022-01-10 04:13:04

The normal Zeeman effect

For the normal Zeeman effect we saw that for electrons in magnetic field , the interaction term of the Hamiltonian operator is:

Where is the angular momentum operator and the magnetic moment is:

And the quantity is known as the gyromagnetic ratio.

This contribution to the Hamiltonian splits the -fold degenerate angular momentum states of the hydrogen atom according to

Where runs over the values .

Contradiction: Experimentally, however, one finds that in atoms with odd atomic number , the splitting is as if were half-integer. Moreover, in contrast to the normal effect, the splitting is different for different levels.

Historical remarks

• Pauli: "The doublet structure of the alkali spectra, as well as the violation of the Larmor theorem, occur due to a peculiar - and not classically describable - ambiguity of the quantum theoretical properties of the valence electron."
• As early as 1921, Compton deduced from the properties of ferromagnetic materials that the electron must possess a magnetic moment.
• Uhlenbeck and Goudsmit: "The electron rotates about its own axis with angular momentum . For this value of the angular momentum, there only two orientations of the angular momentum vector. The gyromagnetic ratio is twice as large for the rotation about its own axis as for the orbital motion."

Summary

The electron possesses an internal angular momentum (called spin) which can assume only the values and in an arbitrarily chosen direction.
The other elementary particles also have spin. Fermions possess half-integer spin, bosons integer spin (including zero).