Evaluation of Matrix Elements

Akiva Novoselsky, Nir Barnea

Matrix elements of two-body operators between many-particle permutational symmetry-adapted functions in hyperspherical coordinates are constructed. The matrix elements are evaluated using the appropriate hyperspherical coefficients of fractional parentage, the Raynal-Revai coefficients, and the hyperspherical recoupling coefficients. We use the power expansion of the two-body operators and obtain an analytic expression for the matrix element of each term. These expressions are studied numerically. The results allow precise evaluations of two-body matrix elements for few-body calculations in nuclear, atomic, and molecular physics.

Hai‐Lun Lin, Yu-Fang Cao

The authors extend the Weyl graphical method to the two-body operator matrix elements in the many-particle system. The evaluation is accomplished by a simple and efficient recursion scheme.

Gintaras Merkelis

The graphical technique of evaluation in the second quantization representation of matrix elements of operators associated with the interactions in atoms is developed. The diagrams corresponding to operators and many-electron states given in terms of irreducible tensorial product of creation and annihilation operators are considered. The general rules for the construction of the diagrams for operators and matrix elements are presented. The procedures of reduction of the diagrams to obtain the algebraic expression are discussed.

Brian L. Silver