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

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.