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Broken Unitary Tableaus, Itinerant Nuclear Spins, and Spontaneous Molecular Symmetry Collapse

  • Willian G. Harter
  • Chris W. Patterson
Part of the Lecture Notes in Chemistry book series (LNC, volume 22)

Abstract

Applications of unitary group (Um) and permutation group (Sn) representations have been the subject of two conferences organized by Professor Jürgen Hinze. The proceedings of the present conference mostly emphasize applications of unitary groups, while the those of the preceeding conference (1) mostly emphasize the permutation groups. A number of papers notably those of Wormer and Sarma in this volume, have reminded us of the inescapable relations between Um and Sn groups. Many of the papers in these volumes have dealt with some number n of indistinguishable spin − 1/2 particles, for example, orbiting electrons, which may occupy some other number m of distinguishable states. The permutation group Sn of distinguishable particles serves as a symmetry group for the system Hamiltonian. The unitary group Um corresponds to the set of all superpositions of the m states which preserve quantum amplitudes. The group Um will be a symmetry group only if the m states remain degenerate in energy. Nevertheless, the Um operations always commute with the Sn permutations so in some sense the two groups are symmetries for each other.

Keywords

Angular Momentum Nuclear Spin Unitary Group Cluster State Permutation Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    J. Hinze (editor) The Permutation Group in Physics and Chemistry, Lecture Notes in Chemistry 12, (Springer Verlag 1979 ).Google Scholar
  2. 2.
    R. S. Berry, Revs. Mod. Phys. 32, 447 (1960);Google Scholar
  3. B. J. Dalton, J. Chem. Phys. 54, 4745 (1971)CrossRefGoogle Scholar
  4. F. Amar, M. E. Kellman, and R. S. Berry, J. Chem. Phys. 70, 1973 (1979).CrossRefGoogle Scholar
  5. 3.
    Ref 1., p. 92–120.Google Scholar
  6. 4.
    K. Fox, M. W. Galbraith, B. J. Krohn, and J. D. Louck Phys. Rev. A 15, 1363 (1977)CrossRefGoogle Scholar
  7. R. S. McDowell, in Laser Spectroscopy III, edited by J. L. Hall and J. L. Carlsten (Springer Verlag 1977 ), p. 102.Google Scholar
  8. 5.
    W. G. Harter, and C. W. Patterson, Phys. Rev. Lett. 38, 224 (1977); J. Chem. Phys. 66, 4872 (1977); Int. J. Quantum Chem. Symposium No. 11, 479 (1977).Google Scholar
  9. 6.
    C. W. Patterson, and W. G. Harter, J. Chem. Phys. 66, 4886, (1977).CrossRefGoogle Scholar
  10. 7.
    W. G. Harter, C. W. Patterson, and F. J. da Paixao, Revs. Mod. Phys. 50, 37 (1978).CrossRefGoogle Scholar
  11. 8.
    H. W. Galbraith, C. W. Patterson, B. J. Krohn, and W. G. Harter, J. Mol. Spectros. 73, 475 (1978).CrossRefGoogle Scholar
  12. 9.
    W. G. Harter, H. W. Galbraith, and C. W. Patterson J. Chem. Phys. 69, 4888, (1978).CrossRefGoogle Scholar
  13. 10.
    W. G. Harter, C. W. Patterson, and H. W. Galbraith J. Chem. Phys. 69, 4896, (1978).CrossRefGoogle Scholar
  14. 11.
    C. W. Patterson, H. W. Galbraith, B. J. Krohn, and W. G. Harter, J. Mol. Spectros. 77, 457 (1979).CrossRefGoogle Scholar
  15. 12.
    W. G. Harter and C. W. Patterson, in Group Theoretical Methods in Physics edited by J. Ehlers et. al., Lecture Notes in Physics 94 (Springer Verlag (1979).Google Scholar
  16. 13.
    K. C. Kim, W. B. Person, D. Seitz, and B. J. Krohn, J. Mol. Spectros. 76, 322 (1979).CrossRefGoogle Scholar
  17. 14.
    A. J. Dorney, and J. K. G. Watson, J. Mol. Spectrosc. 42, 135 (1972).CrossRefGoogle Scholar
  18. 15.
    T. H. Seligman, Ref. 1, p. 178; J. S. Frame, p. 193.Google Scholar
  19. 16.
    W. G. Harter, and C. W. Patterson, J. Math. Phys. 20, 1453 (1979).CrossRefGoogle Scholar
  20. 17.
    Ch. J. Borde’, M. Ouhayoun, and J. Borde’, J. Mol. Spectrosc. 73, 344 (1978).CrossRefGoogle Scholar
  21. 18.
    Ch. J. Borde’, M. Ouhayoun, A. Van Lerberqhe, C. Salomon, S. Avrillier, C. D. Cantrell, and J. Borde’, in Laser Spectroscopy IV, edited by H. Walther and K. W. Rothe, Springer Series in Optical Sciences, ( Springer Verlag 1980 ).Google Scholar
  22. 19.
    C. D. Cantrell, and H. W. Galbraith J. Mol. Spectrosc. 58, 158 (1975).CrossRefGoogle Scholar
  23. 20.
    J. Borde, J. de Physique Lettres 12, L-175, (1978).Google Scholar
  24. 21.
    C. J. Borde, G. Gamy, and B. Decomps Phys. Rev. A20, 254, (1979)Google Scholar
  25. C. J. Borde in Laser Spectroscopy III edited by J. L. Hall, and J. L. Carlsten, Springer Series in Optical Sciences 7 (Springer Verlag, 1977 ) p. 121.Google Scholar
  26. 22.
    W. G. Harter, and C. W. Patterson, Advances in Laser Chemistry, edited by A. H. Zewail (Springer Verlag, 1978 ).Google Scholar
  27. 23.
    W. G. Harter, and C. W. Patterson, Phys. Rev. A19, 2277 (1979).CrossRefGoogle Scholar
  28. 24.
    W. G. Harter, and C. W. Patterson, “Theory of Hyperfine and Superfine Levels in Symmetric Polyatomic Molecules II. Elementary Cases in Octahedral Hexafluoride Molecules”, (submitted to Phys. Rev. A).Google Scholar
  29. 25.
    W. G. Harter, and C. W. Patterson, A Unitary Calculus for Electronic Orbitals, Lecture Notes in Physics 49, (Springer Verlag 1976) p. 139; Phys. Rev. A 13, 1067 (1976).Google Scholar
  30. 26.
    G. W. F. Drake, and M. Schlesinger, Phys. Rev. A 15, 1990 (1977). These authors have related assembly coefficients to Clebsch Gordan coefficients.Google Scholar
  31. 27.
    C. W. Patterson, and W. G. Harter Phys. Rev. A15, 2372 (1977).Google Scholar
  32. 28.
    See for example Fig. 29 p. 66 of Ref. 7.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1981

Authors and Affiliations

  • Willian G. Harter
    • 1
  • Chris W. Patterson
    • 2
  1. 1.School of PhysicsGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Los Alamos Scientific LaboratoryLos AlamosMexico

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