Relativistic calculations for atoms: self-consistent treatment of Breit interaction and nuclear volume effect

Estimates of the ground state energies of several closed-shell atoms and ions with atomic numbers 1<or=Z<or=102 are presented. A relativistic formulation has been employed: energies are obtained as expectation values of the appropriate combination of the Dirac, Coulomb and Breit Hamiltonians with respect to the corresponding Slater determinants of four-component spherical spinor orbitals. Atomic nuclei have been modelled as uniform spherical charge distributions. An expansion method using a kinetically-balanced basis constructed from Gaussian type functions ( approximately r n e - alpha ir2 , where n is an integer and the alpha i form a geometric progression) has been used to formulate the variational problem for the optimal orbital radial functions in each case. The resulting sets of coupled algebraic eigenvalue problems were solved approximately using the self-consistent-field iterative method. The authors' results are compared with those of other workers and with finite-difference calculations carried out specifically for this purpose. They estimate the accuracy of their work to be within a few parts in 10 8 in most cases.