Abstract
It is often accepted that the effects of its neighbourhood on the quantum state of an ion A may be obtained by the model of the crystalline effective field approximation. Within this assumption Stevens has developed a method which provides equivalent operators that facilitate the calculation of the matrix elements of the crystalline field in a given multiplicity. This method has been extended here. We demonstrate that in the expansion of the crystalline field in powers of the electrons coordinates of the ion A - for electrons of the same sub-shell of A - only even terms can contribute. Equivalent operators and matrix elements, in a given multiplicity, are given for these development terms - up to order 6 - and for potential invariant by the operations of one of the thirty-two point-groups. (author) [French] On admet souvent que l'effet de son entourage sur l'etat quantique d'un ion A peut etre obtenu a partir du concept de champ cristallin effectif. Dans le cadre de cette hypothese STEVENS a etabli une methode d'equivalence operatorielle qui facilite l'obtention des elements de matrice de ce champ cristallin dans une multiplicite donnee. Nous generalisons cette methode. Nous demontrons que, dans le developpement du champ
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Boutron, F;
Saint-James, D
[1]
- Commissariat a l'Energie Atomique, Saclay (France). Centre d'Etudes Nucleaires
Citation Formats
Boutron, F, and Saint-James, D.
Irreducible tensor operators and crystalline potentials; Operateurs tensoriels irreductibles et potentiels cristallins.
France: N. p.,
1961.
Web.
Boutron, F, & Saint-James, D.
Irreducible tensor operators and crystalline potentials; Operateurs tensoriels irreductibles et potentiels cristallins.
France.
Boutron, F, and Saint-James, D.
1961.
"Irreducible tensor operators and crystalline potentials; Operateurs tensoriels irreductibles et potentiels cristallins."
France.
@misc{etde_20972226,
title = {Irreducible tensor operators and crystalline potentials; Operateurs tensoriels irreductibles et potentiels cristallins}
author = {Boutron, F, and Saint-James, D}
abstractNote = {It is often accepted that the effects of its neighbourhood on the quantum state of an ion A may be obtained by the model of the crystalline effective field approximation. Within this assumption Stevens has developed a method which provides equivalent operators that facilitate the calculation of the matrix elements of the crystalline field in a given multiplicity. This method has been extended here. We demonstrate that in the expansion of the crystalline field in powers of the electrons coordinates of the ion A - for electrons of the same sub-shell of A - only even terms can contribute. Equivalent operators and matrix elements, in a given multiplicity, are given for these development terms - up to order 6 - and for potential invariant by the operations of one of the thirty-two point-groups. (author) [French] On admet souvent que l'effet de son entourage sur l'etat quantique d'un ion A peut etre obtenu a partir du concept de champ cristallin effectif. Dans le cadre de cette hypothese STEVENS a etabli une methode d'equivalence operatorielle qui facilite l'obtention des elements de matrice de ce champ cristallin dans une multiplicite donnee. Nous generalisons cette methode. Nous demontrons que, dans le developpement du champ cristallin en puissances successives des coordonnees des electrons d'une meme sous-couche de A, seuls les termes pairs doivent etre retenus. Nous donnons ensuite les equivalents operatoriels et les elements de matrice des termes de ce developpement (jusqu'a l'ordre 6), dans une multiplicite donnee, pour des potentiels invariants par les operations de l'un des trente-deux groupes ponctuels. (auteur)}
place = {France}
year = {1961}
month = {Jul}
}
title = {Irreducible tensor operators and crystalline potentials; Operateurs tensoriels irreductibles et potentiels cristallins}
author = {Boutron, F, and Saint-James, D}
abstractNote = {It is often accepted that the effects of its neighbourhood on the quantum state of an ion A may be obtained by the model of the crystalline effective field approximation. Within this assumption Stevens has developed a method which provides equivalent operators that facilitate the calculation of the matrix elements of the crystalline field in a given multiplicity. This method has been extended here. We demonstrate that in the expansion of the crystalline field in powers of the electrons coordinates of the ion A - for electrons of the same sub-shell of A - only even terms can contribute. Equivalent operators and matrix elements, in a given multiplicity, are given for these development terms - up to order 6 - and for potential invariant by the operations of one of the thirty-two point-groups. (author) [French] On admet souvent que l'effet de son entourage sur l'etat quantique d'un ion A peut etre obtenu a partir du concept de champ cristallin effectif. Dans le cadre de cette hypothese STEVENS a etabli une methode d'equivalence operatorielle qui facilite l'obtention des elements de matrice de ce champ cristallin dans une multiplicite donnee. Nous generalisons cette methode. Nous demontrons que, dans le developpement du champ cristallin en puissances successives des coordonnees des electrons d'une meme sous-couche de A, seuls les termes pairs doivent etre retenus. Nous donnons ensuite les equivalents operatoriels et les elements de matrice des termes de ce developpement (jusqu'a l'ordre 6), dans une multiplicite donnee, pour des potentiels invariants par les operations de l'un des trente-deux groupes ponctuels. (auteur)}
place = {France}
year = {1961}
month = {Jul}
}