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

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.