Projection operators in multiconfiguration Dirac-Fock calculations: Application to the ground state of heliumlike ions

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Abstract
The necessity of using projection operators to avoid mixing of positive and negative energy Dirac eigenstates in multiconfiguration Dirac-Fock calculations is discussed. It is shown that convergence problems observed at high Z or when the magnetic interaction was introduced in the self-consistent field (SCF) process are completely due to the absence of such projection operators in previous calculations. It is found that the presence of negative energy states prevented the diagonal Lagrange parameters (orbital energies) of correlation orbitals to approach -∞ when their weights became very small, thus causing the SCF process to fail without projection operators. A method for implementing these projection operators in Dirac-Fock programs is described. A detailed study of the effect of the introduction of projection operators, and of the self-consistent magnetic interaction in the ground state of heliumlike ions is reported. The relative importance of higher-order effects and second-order quantum electrodynamics effects is discussed.