EXTREMUM-PRINCIPLES FOR RELATIVISTIC ATOMIC-STRUCTURE AND SCATTERING - 2-ELECTRON IONS

The time-independent Hamiltonian version of QED provides a foundation for a relativistic description of atomic structure and scattering, with virtual-pair effects treated in a consistent manner. Since the spectrum of the Hamiltonian is bounded from below, the problem of ''variational collapse,'' associated with the existence of negative-energy solutions of the Dirac equation, does not arise. For the same reason, extremum principles of the Rayleigh-Ritz type may be applied. These features are illustrated here in the context of a system consisting of two electrons in an external Coulomb field. An effective Hamiltonian describing this system is constructed in a ladder approximation that accounts for the virtual creation and annihilation of electron-positron pairs. It is shown that this pair contribution to the effective Hamiltonian satisfies a maximum principle and that, consequently, a minimax principle is available for the approximate evaluation of the binding energy of the heliumlike ion. The relation between the present treatment of virtual-pair effects and that based on the Bethe-Salpeter equation in the ladder approximation is clarified.