On the splitting of the Roentgen and optical terms caused by the electron rotation and on the intensity of the cesium lines
 G. Gentile,
 E. Majorana,
 Ennio Arimondo
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Abstract
1. The purpose of this paper is to show that FERMI’s potential allows one to determine a priori and with very good approximation all the energy levels of heavy atoms. This also allows one to calculate with remarkable accuracy, considering its statistical character, the splitting of the various terms. This is of great importance considering that one could not apply SOMMERFELD’s relativistic formula to these splittings, as the phenomenon goes well beyond the scheme of the finestructure theory. Indeed it is well known that one has to use the assumption of the rotating electron which by now has lost its hypothetical character and appears to be well founded on a solid theoretical basis as Dirac’s last paper(1) has shown. Our calculations will be applied to the Roentgen levels of the 3M term of gadolinium (Z = 64) and of uranium (Z = 92) and, in the optical case, to the P terms of cesium (Z = 55).
 Dirac, “Proc. Roy. Soc. (London)”, A 117, 610; 118, 351 (1928).
 Fermi, (1928) Z. Physik 48: pp. 73 CrossRef
 Fermi, (1928) Rend. Acc. Lincei 7: pp. 726
 In general in the classical model there is a normal rosettalike motion both for nonexcited and for excited levels with small azimuth quantum. On the contrary, for certain highly excited levels with large azimuth quantum the BohrSommerfeld orbit splits into two different orbits. One of these reaches the interior of the atom, the other instead is mostly exterior. The model then loses its intuitive meaning.
 Fermi, E. (1927) Rend. Lincei 6: pp. 602
 Thomas, L. H. (1927) Proc. Camb. Phylos. Soc. 23: pp. 542 CrossRef
 Uhlenbeck, G. E., Goudsmit, S. (1925) Naturwiss 13: pp. 953 CrossRef
 Fermi, E. (1930) Z. Phys. 59: pp. 680 CrossRef
 E. Fermi, in Quantentheorie und Chemie, edited by H. Falkenhagen (Leipzig) 1928; reprinted in Collected Papers, Vol. 1 (The University of Chicago Press) 1961.
 Wu, T.Y. (1933) Phys. Rev. 44: pp. 727 CrossRef
 Lee, P. S., Wu, T.Y. (1997) Chin. J. Phys. 35: pp. 742
 Title
 On the splitting of the Roentgen and optical terms caused by the electron rotation and on the intensity of the cesium lines
 Book Title
 Ettore Majorana Scientific Papers
 Book Subtitle
 On occasion of the centenary of his birth
 Pages
 pp 318
 Copyright
 2006
 DOI
 10.1007/9783540480952_1
 Print ISBN
 9783540480914
 Online ISBN
 9783540480952
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SIF, Bologna  SpringerVerlag Berlin Heidelberg
 Additional Links
 Topics
 eBook Packages
 Editors
 Editor Affiliations

 1. Scuola Normale Superiore
 Authors

 G. Gentile
 E. Majorana
 Ennio Arimondo ^{(2)}
 Author Affiliations

 2. NIST, Gaithersburg, MD, USA
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