Relativistic Self-Consistent Fields with Exchange

A relativistic Hartree-Fock calculation of atomic wave functions and energy levels is carried out. The relativistic Hamiltonian is the sum of the Dirac Hamiltonian of the electrons and the retarded Breit interaction. Expressions for the matrix elements of the Hamiltonian are given for closed-shell configurations of electrons, and the relativistic Hartree-Fock equations are derived. A numerical program to compute the Dirac radial functions and energy eigenvalues for an arbitrary closed-shell atom is described. Results obtained for the energies of the ground states of He and Be are found to be in precise agreement with previous nonrelativistic calculations. Results for Ne, Ar, and ${\mathrm{Cu}}^{+}$ are also presented and compared with previous self-consistent-field calculations.