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- W2024157092 abstract "The correspondence between the five d orbitals and the components of the five-dimensional irreducible representation (IR) of the icosahedral group Iis generalized to atomic f orbitals and the seven-dimensional IR of the didodecahedral group D , whose symmetries derive from the non-Euclidean figure possessing 24 regular heptagonal faces meeting in threes at 56 vertices. The group D(limited to rotations of the didodecahedron) is a subgroup of the exceptional Lie group G2 , which Racah used in his analysis of the f shell, but it is not a subgroup of SO (3), the group of rotations in physical space. The sequence O (7)S8 Dprovides an alternative to SO (7)G2 D , where S8is the permutation group that interchanges the eight affinity groups of the didodecahedron among themselves. The analogue for the d shell is O (5)S6 I , where S6permutes the six fivefold axes of the icosahedron and can be used to explain the Coulomb degeneracies of 2 P and 2 H in d3 . To extend these ideas to the f shell, a two-electron Hamiltonian is constructed from operators scalar with respect to both Dand the spin S . The corresponding energy levels are given for the configurations f2and f3 . The absence of SO (3) leads to various coefficients of mixed irrationality. Reflections of the didodecahedron extend Dto Dh , and Dh is used to augment the labelling of the operators and states. It is shown that an interchange of spin and quasispin allows a connection to be made between those parts of the didodecahedral Hamiltonian belonging to the IR (30) of G2and the (30) components of the spin-other-orbit interaction for the atomic f shell." @default.
- W2024157092 created "2016-06-24" @default.
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- W2024157092 date "2000-03-20" @default.
- W2024157092 modified "2023-09-25" @default.
- W2024157092 title "Didodecahedral symmetry for f electrons" @default.
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- W2024157092 doi "https://doi.org/10.1088/0953-4075/33/7/303" @default.
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