No abstract

Expressions for the matrix elements of powers of infinitesimal operators of R. are obtained in a basis reduced a~cording t.o R5 ::J (SU2• x SU2). Operato:s producing th~ basis functions of any weight from those of highest weight are considered. The couplmg and recouplmg procedures for the semistretched and. the other multiplicity-fre~ cases are ~onsidered. By use of projection operators the expressions for the Isoscalar factors of both kmds of semlstretched Clebsch-Gordan coefficients of R., as well as a new formula for the 9j-coefficient of SUo involving only three summation parameters, are obtained. Methods of obtaining the normalized isoscalar factor coupling the basis functions of two symmetrized representations of Rs are discussed.

The algebraic expressions for the matrix elements of symmetric tensor operators (the powers of infinitesimal operators) of the unitary groups in the Gel'fand basis have been studied. The expressions for the isoscalar factors of the related Clebsch-Gordan coefficients, one of the two representations to be coupled being symmetric, as well as the elements of a special recoupling matrix have been found. The supplementary symmetry properties of the isoscalar factors corresponding to the Regge symmetries of the Wigner and 6j coefficients of SU2 have been examined.

AbstractsA theory for using non-orthogonal radial orbitals between shells with identical orbital quantum numbers, in the case of complex configurations, is presented. Construction of the antisymmetric wave function of the whole configuration, with the help of antisymmetrical wave functions of individual shells, is described. General methods of calculating matrix elements of one-and two-electron operators are given.On prCsente une thtorie pour traiter les configurations complexes des atomes en employant des orbitales radiales non-orthogonales entre les couches des tlectrons ayant le m&me nombre quantique orbital. Une mtthode pour construire la fonction d'onde antisymttrique de toute la configuration B l'aide des fonctions d'onde antisymttriques des couches composantes est dtcrite. Les mtthodes gtnCrales pour obtenir des expressions pour les tltments des matrices des opkrateurs B un et deux tlectrons sont donnCes.Es wird eine Theorie fur die Behandlung der Komplexkonfigurationen der Atomen mit Anwendung von nicht-orthogonalen Radialorbitalen zwischen Elektronenschalen mit derselben orbitalen Quantenzahl gegeben. Ein Verfahren fur die Bildung der antisymmetrischen Wellenfunktion der gesamten Konfiguration mit der Hilfe der antisymmetrischen Wellenfunktionen der einzelnen Elektronenschalen wird beschrieben. Die allgemeine Methode zur Auffindung der Ausdrucke fur die Matrixelemente der Einund Zweielektronen-Operatoren wird angegeben.