Foundations of the relativistic theory of many-electron bound states

Most of the existing calculations of relativistic effects in many-electron atoms or molecules are based on the Dirac–Coulomb Hamiltonian H_DC. However, because the electron–electron interaction mixes positive- and negative-energy states, the operator H_DC 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 V_ext 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 V_ext one must consider the effects of virtual-pair creation by the difference potential δU = V_ext ? 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.