Analogy between real irreducible tensor operator and molecular two-particle operator

1997 ◽  
Vol 96 (2) ◽  
pp. 135-139
Author(s):  
Shi-Jun Zhong ◽  
Yin-Gui Wang ◽  
Qian-Er Zhang
Keyword(s):  
Tensor Operator ◽  
Irreducible Tensor ◽  
Irreducible Tensor Operator ◽  
Particle Operator

Application of Truncated Multipolar Expansion Pair Functions in Atomic Structure Calculations. II. Irreducible Tensor Operator Form of the Strongly Orthogonal Pair Functions. Reduction of Orthogonality Constraints

1971 ◽  
Vol 49 (1) ◽  
pp. 118-132 ◽  
Author(s):  
K. Jankowski
Keyword(s):  
Closed Shell ◽  
Tensor Operator ◽  
Irreducible Tensor ◽  
Method Of Calculation ◽  
Irreducible Tensor Operator ◽  
Orthogonality Constraints ◽  
Operator Form ◽  
Orthogonal Pair ◽  
Multipolar Expansion ◽  
Pair Function

The truncated multipolar expansion pair functions (TMEPF) defined recently by Jankowski have been used to formulate an approach which takes into account correlation effects within a pair of electrons in the presence of an N electron sea in a closed shell configuration. An irreducible tensor operator form of the strongly orthogonal pair function components has been derived. The analysis of the expressions obtained leads to a systematic reduction of the orthogonality constraints to be imposed on this class of trial functions. The results of this analysis for several types of pair functions have been given. Finally, the method of calculation of matrix elements between orthogonally projected pair function components in terms of radial integrals is presented.

scholarly journals Irreducible tensor form of three-particle operator for open-shell atoms

Open Physics ◽  
2011 ◽  
Vol 9 (3) ◽  
Author(s):  
Rytis Juršėnas ◽  
Gintaras Merkelis
Keyword(s):  
Angular Momentum ◽  
Symmetric Group ◽  
Open Shell ◽  
Matrix Elements ◽  
Irreducible Tensor ◽  
Tensor Form ◽  
Momentum Theory ◽  
Recoupling Coefficients ◽  
Particle Operator

AbstractA three-particle operator in a second quantized form is studied systematically and comprehensively. The operator is transformed into irreducible tensor form. Possible coupling schemes, identified by the classes of symmetric group S6, are presented. Recoupling coefficients that make it possible to transform a given scheme into another are produced by using the angular momentum theory combined with quasispin formalism. The classification of the three-particle operator which acts on n = 1, 2,..., 6 open shells of equivalent electrons of atom is considered. The procedure to construct three-particle matrix elements are examined.

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