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| Titel: |
The group-theoretical structure of the atomic d shell and the energies of the corresponding terms |
| Auteur: |
King, R. Bruce |
| Verschenen in: |
Molecular physics |
| Paginering: | Jaargang 104 (2006) nr. 12 pagina's 1855-1860 |
| Jaar: |
2006-06-20 |
| Inhoud: |
The icosahedral symmetry I ≈ A5 of the atomic d shell can arise from the symmetries of the five-dimensional d orbital space through the subgroup chain SO(5) ⊃ SO(3) ⊃ I or O(5) ⊃ S6 ⊃ S5 ⊃ I. In the latter case the symmetric group S5 can be generated from I ≈ A5 by addition of the period 4 kaleidoscope operator K, which mixes the d orbitals with m = ±1 and those with m = ±2. Furthermore, separation of the dn configurations into two sets according to the parity of n (even or odd) and the irreps of SO(5) is found to lead to new relationships between the multiplicities and seniorities of the corresponding terms. Thus the sums of the seniorities and multiplicities for even and odd n for a given irrep of SO(5) lead to a constant, namely 12. Furthermore, new pseudodegeneracies are found to arise when the energy expressions of pairs of otherwise equivalent terms with different seniorities for a given dn are adjusted to remove the radicals arising from solution of the quadratic secular equation. In addition to the well-known 2H/2P degeneracy for d3, 3F/3P degeneracies are found for d4 and a 2D/2S pseudodegeneracy is found for d5. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 14 van 17 gevonden artikelen
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