Many-particle coefficients of fractional parentage

The relation between the CFP with a detached electrons and the reduced matrix elements of operator q (lNfiLS generating [see (15.4)] the 7-electron wave function is established in exactly the same way as in the derivation of (15.21). Only now in the appropriate determinants we have to apply the Laplace expansion in terms of a rows. The final expression takes the form 

For the phase factor, we have used the fact that a and 2S2 have the same parity. 

the dependence of the phase factor on the number of electrons is determined by the number of commutations of appropriate creation operators. 

The CFP with a detached electrons can also be expressed in terms of the submatrix element of the irreducible tensorial product of a annihilation operators (15.10), for which we have 

Of great importance is a special case of the above coefficients - the CFP with two detached electrons  

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