Foundations of the relativistic theory of many‐electron bound states

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Abstract
Most of the existing calculations of relativistic effects in many‐electron atoms or molecules are based on the Dirac–Coulomb Hamiltonian HDC. However, because the electron–electron interaction mixes positive‐ and negative‐energy states, the operator HDC has no normalizable eigenfunctions. This fact undermines the quantum‐theoretic rationale for the Dirac–Hartree–Fock (DHF) equations and therefore that of the relativistic configuration‐interaction (RCI) and multiconfiguration Dirac–Fock (MCDF) methods. An approach to this problem based on quantum electrodynamics is reviewed. It leads to a configuration‐space Hamilton H which involves positive‐energy projection operators dependent on an external potential U; identification of U with the nuclear potential Vext corresponds to use of the Furry bound‐state interaction picture. It is shown that the RCI method can be reinterpreted as an approximation scheme for finding eigenvalues of a Hamiltonian H, with U identified as the DHF potential; the theoretical interpretation of the MCDF method needs further clarification. It is emphasized that if U differs from Vext one must consider the effects of virtual‐pair creation by the difference potential δU = Vext − U; an approximate formula for the level‐shift arising from δU is derived. Some ideas for dealing with the technical problems introduced by the projection operators are discussed and relativistic virial theorems are given. Finally, a possible scheme for adapting current MCDF methods to Hamiltonians involving projection operators is described.

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