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  • 1
    Electronic Resource
    Electronic Resource
    Communications in mathematical physics 36 (1974), S. 157-170 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract In various tabulations of such spectroscopic coefficients as the matrix elements of tensor operators or fractional parentage coefficients, it is found that many entries are unexpectedly zero. A survey is made of all cases that occur in the atomicf shell and that involve the 7-dimensional vector representation of the groupG 2. Direct explanations are given in terms of the group structure of the electronic configurations that comprise the shell. The techniques used depend on a splitting of the state space into “spin-up” and “spin-down” parts, and, for other cases, the extensive use of the methods of second quantization. TheF terms of the atomicf shell are found to split into three classes. The separation that this classification provides for the twoF terms belonging to the irreducible representation (31) ofG 2 coincides with Racah's separation. An improved separation of theH states of (31) is described.
    Type of Medium: Electronic Resource
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