Quasi-Particle Groups in Atomic Shell Theory

  • B. R. Judd


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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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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