Breit interaction for the helium ground state

The Breit interaction in second-quantized form, written in normal order relative to a closed-shell core is 

The first-order Breit correction, which grows approximately as Z , is compared with the Hartree-Fock energy for helium-like ions in Fig. 6. 

Owing to its small size, the dominant correlation corrections to the Breit interaction are those associated with one Breit and many Coulomb terms. As mentioned earlier, these dominant corrections can be obtained from MBPT formulas such as those in Eqs. (102) and (103) by substituting Vijki — Uyw - - hijki and linearizing in hijki- The second-order (one Breit-one Coulomb) correlation energy from Eq. (92) is 

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