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First edition, extremely rare offprint, of this important attempt to explain quantitatively the spectrum of helium on the basis of the Bohr-Sommerfeld quantum theory; its failure forced theorists to accept that the old quantum theory was untenable which in turn led to the invention of quantum mechanics two years later. Bohr wrote to Born that "the result [of this paper] is certainly of great importance as it indicates the inadequacy of the present foundation of quantum theory in so far as it concerns systems with several electrons" (Kragh, p. 257). "The work that Born and Heisenberg completed at Göttingen was a mathematically rigorous and completely general investigation of all possible types of electronic motion in excited helium. The aim was to derive theoretical spectral terms and, by comparing them to the terms inferred from the observed spectral lines, draw conclusions with regard to the viability of quantum atomic theory . . . The verdict was brief and unequivocal: 'The result of our investigation is totally negative' (p. 242). In conclusion, they stated that there were only two ways out of the problem. Either the quantum conditions were wrong, and one would, for example, have to consider non-integral values for the azimuthal quantum numbers, or the motion of the electrons in the stationary states did not follow the laws of mechanics . . . Confessing that 'I don't seem to get any closer to the great mystery of the quanta, in spite of all my efforts,' Born reported the failure of the helium calculation to Einstein: 'We have been looking at perturbation theory to determine whether it is possible to observed term values from Bohr's models by exact calculation. But it is quite certainly not the case, as was demonstrated with helium' . . . Bohr's attitude is of particular interest. Well aware of the new calculations from Göttingen, he had commented on them even before the publication of the Born-Heisenberg paper, namely in a long paper on atomic structure that appeared in Annalen de Physik. In this paper he dealt at some length, if only qualitatively, with the helium atom, and in a footnote he referred to the forthcoming work of Born and Heisenberg. 'Not only is no explanation obtained of the non-occurrence of combinations between ortho- and parhelium atoms, but not even an approximate value of these terms can be obtained,' he wrote. Moreover, 'This investigation may therefore be particularly well suited to provide evidence of the fundamental failure of the laws of mechanics to describe the finer details of the motion of systems with several electrons' . . . Bohr agreed that the existing quantum theory had to be revised, but not that it was fundamentally wrong . . . . Born was of the opinion that the 'helium catastrophe' should have more drastic consequences, although he could not say exactly what consequences. In his contribution from the summer of 1923 to the Bohr issue of Naturwissenschaften, he dealt with the helium problem and the failure of applying mechanics to the stationary states of this atom. It followed, he said, that atoms could be likened to planetary systems only in a very limited sense. 'However,' he went on in the style of Bohr, 'the progress of quantum theory is not therefore blocked, for it will rather gain new strength by the existing contradictions. It becomes more and more likely that that not only new assumptions in the usual sense of physical hypotheses will be necessary, but the entire system of concepts of physics must be rebuilt from the ground up'" (ibid., pp. 255-7). This is precisely what Heisenberg began in his 1925 paper on quantum mechanics. Not on OCLC, no copies in auction records. Kragh, Niels Bohr and the Quantum Atom, 2012. 8vo, pp. 229-243, [1, blank]. Original printed wrappers (minor creasing, stamp of Dunbar Laboratory, Harvard, to bottom margin of rear cover).
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