Unit tensors in a relativistic approach

The analogue of unit tensor (5.23) in j-space may be defined as follows  

In order to find expressions for relativistic matrix elements of the energy operator we have to utilize the following formula for two-particle scalar operators  

The need to have only one sort of unit tensor (7.2) and its sum (7.4) is conditioned by the fact that, unlike a non-relativistic case, where we 

It is interesting to emphasize that submatrix elements (7.5) are proportional to the CFPs with two detached electrons, defined by (9.15), namely 

Let us present in conclusion the expression for the submatrix element of scalar product (7.3), necessary while calculating relativistic matrix elements of the energy operator. It is as follows  

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In order to derive a relativistic version of the elecfiic-dipole / <—) f transitions the concept of Sandras and Beck [59] is applied to include new effects in an effective way. This means that every unit tensor operator analyzed in the non-relativistic approach has to be replaced prior to the partial closure by a double unit tensor operator that acts within the spin (k) - orbital (k) space. The transformation is as follows. 

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