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My understanding is that explaining ortho- and para- helium spectral lines was a key motivation for Heisenberg's new quantum theory. For example, Birthwistle's 1928 "The New Quantum Mechanics", Chapter XXVI states:

It is well known that the spectral terms of helium can be divided into two sets such that no term of the one will combine with a term of the other to produce a spectral line. … One set by its transitions gives the 'para helium' lines … the other set gives the 'ortho helium' lines …

Since it is "well known", Birthwistle give no sources. He further goes on to say

The obvious failure of the classical mechanics and the correspondence principle to solve the problem of a nucleus with two outer electrons was one of the factors which compelled Heisenberg to seek for a new quantum mechanics …

When and how was the helium spectrum measured sufficiently to establish the existence of two sets of line and the challenge for Bohr's quantum mechanics recognized? Are there any good articles or books that discuss this?

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By 1928, Stark had an article in the Annelen der Physik on the intensities of the Ortho- and Para-series in helium.

In that article, Stark references a 1924 Astrophysical Journal paper by Lyman, in which Lyman summarizes his conclusions on the He spectrum based on nearly a decade worth of work.

As one example of the efforts to explain Helium, I would point to Sommerfeld's 1924 paper in the Journal of the Optical Society of America.

Remember, this was early in the quantum era - one needed good data, good theory, and good ideas to straighten it all out.

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There is also nice discussion with lots of historic references in an article by Helge Krah from 2009 ('The Solar Element: A Reconsideration of Helium's Early History').

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