A method for the solution of the pair equation, by summation over a complete and finite basis set, is presented. The basis set is obtained by diagonalization of a discretized Hermitian one-particle Hamiltonian. The number of operations required to solve the radial pair equation is proportional to N where N is the number of radial lattice points used. An application to the ground state of helium, evaluating the total energy to an accuracy of a few parts in 10, is presented. The method is equally well applicable to the study of pair correlation in many-electron atoms.

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The Breit interaction has been treated together with the Coulomb interaction in a self-consistent way, leading to modified occupied orbitals (Dirac-Fock-Breit orbitals), which are analysed. The arguments against the inclusion of the Breit interaction to higher orders are discussed, as well as the advantages in doing so. The new orbitals are then used to calculate the electric dipole moment (EDM) in Tl and are found to lead to a 2% reduction of the EDM enhancement factor.

The ratio of the atomic electric dipole moment (EDM) to a possible electron EDM has been calculated for the ground states of Cs, Xe and Hg, including to all orders the diagrams that involve only single excitations, while neglecting correlation effects, which require the simultaneous excitation of two or more electrons. The alkali atoms are known to have large enhancement factors and as a test of the procedure, a calculation was performed for the Cs ground state. The lowest experimental limit for an atomic EDM, so far has been established for the ground state of Xe, which is a closed-shell system, where the simple mechanisms for producing an atomic EDM from an electronic one are not available, but the interaction with the nuclear magnetic moment may still give an atomic EDM, which is here found to be about 10−3 of the electron EDM. For the heavier atom Hg, the effect is an order of magnitude larger.

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