The relativistic pair equation and related fundamental problems

This is the authors' abstract. We don't add key points for this paper.

By the use of projection operators, defined in Dirac space, it is shown how a relativistic pair equation, correct to order α2 Ry, can be constructed. It is pointed out how the Brown-Ravenhall disease (continuum dissolution) is rigorously avoided with this procedure. The pair equation treats correlation relativistically starting from a suitable choice of a fully relativistic one particle description of the atom. Second order contributions to the energy from the electrostatic correlation have been calculated for the 1s2 ground state of two-body systems with (Z = 2, 10). The starting point has been either hydrogen-like wavefunctions or Dirac-Fock orbitals. Excitations to s2, p2 and d2 have been treated and an unexpected behaviour of the p1/22 excitation relative to the p3/22 one is discussed. By iterative solutions of the exact pair equation a non-perturbative treatment of the two-body part of the static Coulomb interaction is obtained. This procedure has been used for s-excitation and a comparison of the relativistic and non-relativistic behaviour is made.