Quasi-Particle Groups in Atomic Shell Theory

  • B. R. Judd

Abstract

In 1968 some bizarre features of atomic shell theory were noticed. One such appeared when efforts were made to generalize the use of G2 for atomic electrons. Racah had demonstrated the great utility of this exceptional Lie group in his classic paper on the Coulomb energies off electrons,1 but it was known that no analogous group existed for electrons with higher ℓ. However, the G2 classification of the states of the f shell could be accomplished by diagonalizing a two-electron operator belonging to the irreducible representation (irrep) (111) of S0(7). It can be shown that such an operator is necessarily a scalar with respect to G2 too. For g electrons we can form an operator that is an S0(3) scalar and which also belongs to (1111) of S0(9). As such, it is an analog of the G2 scalar although no actual analog of the group itself exists. When the operator was diagonalized for the states of maximum multiplicity (maximum S) of gN, many eigenvalue repetitions were noticed.2 Moreover, several fractional parentage coefficients vanished for no obvious reason. Armstrong found that corresponding simplifications occurred in the h shell.3

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References

  1. 1.
    G. Racah, Theory of complex spectra. IV, Phys. Rev., 76: 1352 (1949).Google Scholar
  2. 2.
    B. R. Judd, Atomic g electrons, Phys. Rev., 173: 40 (1968).Google Scholar
  3. 3.
    L. Armstrong, private communication (1968).Google Scholar
  4. 4.
    B. R. Judd and J. P. Elliott, “Topics in Atomic and Nuclear Theory,” Caxton Press, Christchurch, New Zealand (1970), pp. 47 – 50.Google Scholar
  5. 5.
    B. R. Judd, Group theory in atomic spectroscopy, in “Group Theory and Its Applications,” E. M. Loebl, ed., Academic Press, New York (1968).Google Scholar
  6. 6.
    L. Armstrong and B. R. Judd, Quasi-particles in atomic shell theory, Proc. Ry Soc. London, A315: 27 (1970); Atomic structure calculations in a factorized shell, Proc. Roy. Soc. London, A315: 39 (1970).Google Scholar
  7. 7.
    B. Gruber and M. Samuel Thomas, Symmetry chains for the atomic shell model. I. Classification of symmetry chains for atomic configurations,KinamA2: 133 (1980).Google Scholar
  8. 8.
    J. P. Elliott and J. A. Evans, A new classification for the jn configuration, Phys. Lett., 31B: 157 (1970).Google Scholar
  9. 9.
    J. C. Parikh, The role of isospin in pair correlations for configurations of the type (j)N, Nucl. Phys., 63: 214 (1965)Google Scholar
  10. 10.
    B. H. Flowers, Studies in jj-coupling. I. Classification of nuclear and atomic states,Proc. Roy. Soc. LondonA212: 248 (1952).Google Scholar
  11. 11.
    K. T. Hecht and S. Szpikowski, On the new quasiparticle factorization of the j-shell, Nucl. Phys., A158: 449 (1970).Google Scholar
  12. 12.
    S. Feneuille, Traitment des configurations (d + s)N dans le formalism des quasi-paricules, J. Physique, 30:923 (1969).Google Scholar
  13. 13.
    M. J. Cunningham and B. G. Wybourne, Quasiparticle Formalism and atomic shell theory II. Mixed Configurations,J. Math Phys., 11:1288 (1970).Google Scholar
  14. 14.
    B. R. Judd, Algebraic expressions for classes of generalized 6—j and 9—j symbols for certain Lie groups, in Proceedings of the XVI International Colloquium on Group Theoretical Methods in Physics, Varna, Bulgaria (1987).Google Scholar

Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • B. R. Judd
    • 1
  1. 1.Department of Physics and AstronomyThe Johns Hopkins UniversityBaltimoreUSA

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