Correlation in a relativistic framework

Abstract

By the use of projection operators, defined in Dirac space, it is shown how a relativistic pair equation, correct to order α 2Ry, 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 1s 2 ground state of some two-body systems. The starting point has been either hydrogen-like wave functions ( Z = 2, 10) or Dirac-Fock orbitals ( Z 10−60). Excitations to s 2, p 2, d 2 and f 2 have been treated and an unexpected behaviour of the p 2 1 2 excita P 2 3 2 one is discussed. By iterative solutions of the exact pair equation a nonperturbative treatment of the two-body part of the s Coulomb interaction is obtained. This procedure has been used for s excitations ( Z = 2−20) and a comparison of the relativistic and nonrelativistic behaviour is made.