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G. H. Shortley and B. Fried, Phys. Rev. 54, 749 (1938).
E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge Univ. Press, Cambridge, England, 1935), especially Chaps. 6, 7, 10, 11, 13.
J. C. Slater, Quantum Theory of Atomic Structure (McGraw-Hill Book Company, Inc., New York, 1960), especially Chaps. 12, 13, 24. For brief discussions of the theory, see also H. G. Kuhn, Atomic Spectra (Academic Press, Inc., New York, 1962), Chap. V, and Ref. 25, Sec. II.
K. B. S. Eriksson, Phys. Rev. 102, 102 (1956); Arkiv Fysik 13, 303 (1958).
L. J. Radziemski and K. L. Andrew, J. Opt. Soc. Am. 55, 474 (1965).
Y. G. Toresson, Arkiv Fysik 18, 389 (1960).
W. C. Martin, J. Opt. Soc. Am. 49, 1071 (1959).
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B. Edlén and J. W. Swensson, reported at Atomic Spectroscopy Symposium, Argonne National Laboratory, June 1961.
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K. B. S. Eriksson and I. Johansson, Arkiv Fysik 19, 235 (1961).
K. B. S. Eriksson, Arkiv Fysik 19, 229 (1961).
L. Minnhagen, Arkiv Fysik 18, 97 (1960).
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J. L. Tech, J. Res. Natl. Bur. Std. 67A, 505 (1963).
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See Ref. 4, p. 123.
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We shall not be much interested in M degeneracy in this paper and will speak only in terms of J degeneracies, considering there to be only one state per value of J.
G. Racah, Phys. Rev. 63, 367 (1943).
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See Ref. 28, p. 41, or Ref. 29, Eq. (1–21).
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K. Smith and J. W. Stevenson, Argonne National Laboratory Reports ANL-5776 and ANL-5860.
Actually, these are already available in the literature for most cases of interest (see Refs. 4, 5).
Small values of ζf would, of course, also remove the degeneracy (see Table II).
G. H. Shortley, Phys. Rev. 44, 670 (1933).
Note that this is different from the definition of purity used in discussing Figs. 4 and 5, and accounts for the increase in apparent LS and LK purity in going from the 4f to the 6f configuration.
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Ref. 25, Tables 38 and 42 and Fig. 12.
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See Ref. 29, Eq. (4-4).
The diagonal elements in any representation can be calculated directly by means described by J. C. van den Bosch in Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1957), Vol. XXVIII, pp. 305 ff, but the off-diagonal elements are readily found only by transforming the g matrix from the LS representation.
Data from C. E. Moore, Natl. Bur. Std. (U.S.) Circ. No. 467 1 (1949), 2 (1952). Data for Xe I have been omitted because they are badly perturbed: J. B. Green, E. H. Hurlburt, and D. W. Bowman, Phys. Rev. 59, 72 (1941).
J. B. Green, Phys. Rev. 52, 736 (1937).