Simplified components of the spin-other-orbit interaction near the middle of the atomic f shell
Titel:
Simplified components of the spin-other-orbit interaction near the middle of the atomic f shell
Auteur:
Judd, B. R. Hansen, J. E.
Verschenen in:
Molecular physics
Paginering:
Jaargang 102 (2004) nr. 11-12 pagina's 1207-1211
Jaar:
2004-06-10
Inhoud:
To honour the memory of Brian Garner Wybourne, an analysis is presented of three components of the spin-other-orbit interaction for f electrons using the kind of Lie groups he would have been familiar with. The components have been named z6, z8 and z10. They all belong to the irreducible representation (IR) (30) of Racah's group G2. Near the middle of the f shell it is often found that fewer independent blocks of numbers are needed to express their matrix elements than the Wigner-Eckart theorem, generalized to the IRs U of G2, would indicate. Each block corresponds to a given U and U ', and possesses rows and columns labelled by the angular momenta L and L'. The number of independent blocks would be expected to be given by Racah's multiplicity function c(UU ' (30)); but near the middle of the shell the number c(UU ' (20)) (or less) often suffices. For this to occur, z8 and z10 have to be replaced by linear combinations corresponding to IRs of the types (20)×(10) and (21)×(10) of the direct product group G2A×G2B, where A and B refer to electrons with their spins up (A) and spins down (B). A detailed example is provided by the IR (31) of G2, which occurs in the configurations f 5 through f 9. In addition, two antiHermitian operators (za6 and za7) that also belong to the IR (30) of G2 are discussed.
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