OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Vol. 1, Iss. 2 — Apr. 1, 1984
  • pp: 255–260

Orthogonalized operators for the ƒ shell

B. R. Judd and H. Crosswhite  »View Author Affiliations


JOSA B, Vol. 1, Issue 2, pp. 255-260 (1984)
http://dx.doi.org/10.1364/JOSAB.1.000255


View Full Text Article

Acrobat PDF (625 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Orthogonalized operators are introduced in the atomic configurations ƒN in order to yield parameters that are more precisely defined and more stable than the conventional ones. Of the four Racah operators e0, e1, e2, and e3, only e1 needs adjusting. The set of two-electron scalars is made complete by the generalized Trees operators eα′, eβ′, and e υ′. Of the three-electron scalars ti, only t2 requires alteration. The theory is illustrated for ƒ3 by adding the orthogonalized operators in successive steps and comparing the fits with those obtained if the conventional operators are used.

© 1984 Optical Society of America

Citation
B. R. Judd and H. Crosswhite, "Orthogonalized operators for the ƒ shell," J. Opt. Soc. Am. B 1, 255-260 (1984)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-1-2-255


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge U. Press, New York, 1935).
  2. R. E. Trees, "Configuration interaction in Mn II," Phys. Rev. 83, 756–760 (1951); "Term values in the 3d54s configuration of Fe III," Phys. Rev. 84, 1089–1091 (1951).
  3. K. Rajnak and B. G. Wybourne, "Configuration interaction effects in lN configurations," Phys. Rev. 132, 280–290 (1963).
  4. B. R. Judd, J. E. Hansen, and A. J. J. Raassen, "Parametric fits in the atomic d shell," J. Phys. B 15, 1457–1472 (1982). The entry −6√14 in the sixth column of Table A.6 of this paper should be interchanged with the zero standing to its immediate right.
  5. B. R. Judd, "Operator averages and orthogonalities," in Proceedings of the XII Symposium on Group Theoretical Methods in Physics, Trieste (1983), in Lecture Notes in Physics (Springer-Verlag, New York, 1984).
  6. G. Racah, "Theory of complex spectra. IV," Phys. Rev. 76, 1352–1365 (1949).
  7. G. Racah, "Group theory and spectroscopy," in Springer Tracts in Modern Physics (Ergebnisse der Exakten Naturwissenschaf-ten) (Springer-Verlag, New York, 1965), Vol. 37.
  8. P. Uylings (alias Uijlings), Zeeman Laboratorium, Amsterdam, the Netherlands (personal communication).
  9. D. J. Newman, "Operator orthogonality and parameter uncertainty," Phys. Lett. A 92, 167–169 (1982); Department of Physics, Hong Kong University, Hong Kong (personal communication).
  10. B. R. Judd, "Three-particle operators for equivalent electrons," Phys. Rev. 141, 4–14 (1966).
  11. J. Sugar, "Analysis of the third spectrum of praseodymium," J. Opt. Soc. Am. 53, 831–839 (1963); H. Crosswhite, H. M Cross-white, and B. R. Judd, "Magnetic parameters for the configuration ƒ3," Phys. Rev. 174, 89–94 (1968).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited