The relativistic pair equation and related fundamental problems

Abstract

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.