Operators in quasispin space of separate shells

Since the wave function of a complex configuration is constructed by vectorial coupling of the orbital and spin momenta of individual shells, one-shell quantum numbers a,y,L,S, (just like the intermediate momenta) are additional characteristics for the wave function of entire configuration (17.33). Specifically, the two-shell wave function 

Operators corresponding to physical quantities can also be expanded in terms of irreducible tensors in the quasispin space of each individual shell. To this end, it is sufficient to go over to tensors (17.43) and next to provide their direct product in the quasispin space of individual shells. This procedure can conveniently be carried out for a representation of operators such that the orbital and spin ranks of all the one-shell tensors are coupled directly. Here we shall provide the final result for the two-particle operator of general form (14.57) 

It has been shown in the previous section how the submatrix elements of irreducible tensorial products of creation and annihilation operators can be expressed in terms of pertinent one-shell submatrix elements. The submatrix elements of the operators G1-G7 are also defined in terms of the same quantities. Since the quasispin ranks from different shells that 

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Operators in quasispin space of separate shells 17.4 Operators in quasispin space of separate shells... 

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