Abstract
The formulae of Redmond are used to construct expressions for the fractional parentage coefficients relating the configurations l 3 and l 2 . The explicit occurrence of godparent states is avoided for the quartet states of f 3 and also for a sequence of doublet states. The latter are defined by the set of quantum numbers f 3 WUSLJJ 2 , where W and U are irreducible representations of the groups R 7 and G 2 . Matrix elements of the type ( f 3 WUSL || U k || f 3 W'U'SL' ), where U k is the sum of the three irreducible tensor operators u k corresponding to the three f electrons, are tabulated for k = 2, 4 and 6 and for all values of W, U, S and L .
Keywords
Tensor (intrinsic definition)Irreducible representationMathematicsMatrix (chemical analysis)ElectronCombinatoricsTensor productType (biology)PhysicsSequence (biology)Tensor operatorQuantum numberPure mathematicsMathematical physicsAlgebra over a fieldQuantum mechanicsChemistry
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Publication Info
- Year
- 1959
- Type
- article
- Volume
- 250
- Issue
- 1263
- Pages
- 562-574
- Citations
- 31
- Access
- Closed
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Cite This
Brian R. Judd
(1959).
The matrix elements of tensor operators for configurations of three equivalent electrons.
Proceedings of the Royal Society of London A Mathematical and Physical Sciences
, 250
(1263)
, 562-574.
https://doi.org/10.1098/rspa.1959.0083
Identifiers
- DOI
- 10.1098/rspa.1959.0083