Induced operator orthogonality across an atomic shell
- 28 July 1990
- journal article
- Published by IOP Publishing in Journal of Physics B: Atomic, Molecular and Optical Physics
- Vol. 23 (14) , 2197-2204
- https://doi.org/10.1088/0953-4075/23/14/008
Abstract
The establishing of operator orthogonality for atomic configurations C by means of group theory is extended to operators Hi requiring arbitrary multiplicity labels to distinguish them. By including the zero-electron operator in the set of orthogonal operators, each N-electron operator can be constructed to belong to the irreducible representation (irrep) (1N041+2-2N-1N) of SU(41+2), with the result that: (a) operator orthogonality for C=1n is equivalent to a relation between 3-j symbols for the group SU(41+2), and (b) the effect of electron-hole conjugation is simplified and no quasispin ranks of mixed parity appear. A second kind of orthogonality relation, in which the running index is the operator label i, yields new relations satisfied by the matrix elements of the orthogonal operators. The dependence of operator normalisation on N and n is derived from a group-theoretical formula of Hecht (1975) and confirmed by an approach using fractional parentage. Generalisations to other atomic configurations are briefly considered.Keywords
This publication has 20 references indexed in Scilit:
- Least-squares fitting of parametrized Hamiltonians to energy levels: An investigation into alternative strategiesComputers in Physics, 1989
- Parametric fitting with orthogonal operatorsPhysica Scripta, 1988
- Parametric fitting to dN configurations using orthogonal operatorsNuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 1988
- Parametric fitting to 2pN3d configurations using orthogonal operatorsJournal of Physics B: Atomic and Molecular Physics, 1987
- Orthogonal operators applied to term analysis residues for Fe VI 3d24pJournal of Physics B: Atomic and Molecular Physics, 1987
- Observation of four-body effects in atomic spectraJournal of Physics B: Atomic and Molecular Physics, 1985
- Fine-structure analyses with orthogonal operatorsJournal of Physics B: Atomic and Molecular Physics, 1985
- Orthogonal scalar operators for pNd and pdNJournal of Physics B: Atomic and Molecular Physics, 1985
- Orthogonalized operators for the ƒ shellJournal of the Optical Society of America B, 1984
- A simple class ofU(N) Racah coefficients and their applicationCommunications in Mathematical Physics, 1975