Algebraic expressions for CFP of the fN uiU2 vLS shell

It is well known that even for three /-electrons the classification of terms by the seniority number turns out to be insufficient. In this case, the exclusive group G2 has been applied with success [24], although it is still 

We need the following scalar of the G2 group, i.e. an operator that commutes with all the generators of this group  

The method used to establish the algebraic formulas for CFP is, in broad outline, as follows if at least one wave function is available that is characterized by the quantum numbers (111112) and L, then all the remaining functions with the same quantum numbers can be constructed 

Accordingly, for each ( i 2) the problem comes down to the construction of one wave function with a given L. At (111112) = (00), (10), (20) and (11) these quantities are known - these are the wave functions of one and two equivalent electrons with v = 0, 1, 2. In order to construct wave functions with other (U1U2) we make use of the fact that at a given v the wave function with maximal L has a uniquely defined characteristic of the G2 group. 

Wave functions with the same Q, S, ( i 2), but different L, can be obtained using one of the generators of the G2 group, namely IF 050, as follows  

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