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

TL;DR

This paper develops a method to express three-particle operators in irreducible tensor form for open-shell atoms, enabling better understanding and calculation of atomic interactions involving multiple electrons.

Contribution

It introduces a systematic approach to transform three-particle operators into irreducible tensor form and provides recoupling coefficients using angular momentum theory and quasispin formalism.

Findings

Derived irreducible tensor form for three-particle operators.

Presented coupling schemes based on symmetric group classes.

Outlined procedures for constructing three-particle matrix elements.

Abstract

The three-particle operator in a second quantized form is studied. The operator is transformed into irreducible tensor form. Possible coupling schemes, distinguished by the classes of symmetric group \mathrm{S_{6}}, are presented. Recoupling coefficients, which allow one to transform given scheme into another, are produced by using the angular momentum theory, combined with quasispin formalism. The classification of 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.