Pais, in his "Inward Bound", describes the early history of spin. He tells us that Goudsmit and Uhlenbeck interpreted Pauli's "doubled valuedness" as spin, while in turn Pauli re-interpreted a pre-existing, so-called "inner" quantum number as describing a property of the valence electron.

Before Pauli's reinterpretation, Sommerfeld, Landé, and Heisenberg all seem to have written about this number, and they all thought it had something to do with the "inner parts" of the atom (not the valence electron). But who introduced it, and why?

I would guess it was Sommerfeld who introduced it - in his Munich lectures in 1916 - but as far as I can tell, he only published anything about it in 1929 in Volume II of his "Atomic structure..." (which he says are based on these lectures) relatively long after the re-interpretation as intrinsic spin of the electron. Did he or did anyone introduce this "inner quantum number" in a published article before said Volume II, and before it turned into electron spin? Pais says that this quantum number is referred to as the "inner quantum number" and mentions articles by Landé and Heisenberg's very first paper, but I think neither introduced this inner quantum number for the first time, or did they?

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    $\begingroup$ The Big Chemical Encyclopedia site states "Sommerfeld went on to discover the third or inner, quantum number, thus enabling the British physicist Edmund Stoner to come up with an even more refined set of electronic configurations in 1924.", suggesting that Sommerfeld had made public (if not published) his discovery before the 1929 publication of Volume II - possibly only in lectures. $\endgroup$
    – nwr
    Oct 3, 2022 at 22:45


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