Tensors in the space of total quasispin and their submatrix elements

6 Tensors in the space of total quasispin and their submatrix elements 

The representation of the wave function in the scheme of coupled quasispin momenta calls for the introduction of operators (17.43) whose quasispin ranks from different shells would be coupled as well. 

The tensors on the right sides of (17.59) and (17.60) are given by (17.9) and are generally introduced for mixed configurations by linear combinations of the tensors and Wj K l2, h). Accordingly, these 

following Chapter 15, we shall examine tensorial products of two-shell operators. Consider the product (K /j) x 

We next put the orbital ranks on the left side of (17.61) equal to zero k = k = ki = 0), and then construct a set of equations by selecting the values of spin and quasispin ranks so that on the left side of this equation we have operators with known eigenvalues. In the case of complete scalars K1 = ki =k, selecting the values of ranks the same as they were in Chapter 15 and solving the resultant set of equations for the sum of a given structure of spin and quasispin ranks, we find 

II = 0. These tensors, in addition to the triple tensors inside the shell introduced in Chapter 15, will be the basic standard quantities in our further treatment. 

Exchanging the operators dqllS and a, 2S) and recoupling the momenta yields [121] 

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