Relativistic many-body calculations of energies of Mg I, Al II, Al I, Hg I, Tl II, Tl l, Pb I, Bi II and Bi I

Energies of the low-lying excited states of six atomic systems with two electrons above the core (Mg I, Al II, Hg I, Tl II, Pb I, and Bi II) and three systems with three electrons above the core (Al I, Tl I, and Bi I) are determined to second order in relativistic many-body perturbation theory using frozen-core Dirac-Hartree-Fock orbitals as a basis set. In the present report, the Breit interaction is included to first order only. Diagonalization of the effective Hamiltonian is carried out using two methods: (I) the symmetric first-order Hamiltonian (including both Coulomb and Breit interactions) is diagonalized and then the second-order correlation is determined using the first-order eigenvectors; (II) the first-order (Coulomb plus Breit) together with the non-symmetric second-order effective Hamiltonian is diagonalized. Different model spaces are considered. Contributions from the three-electron interaction are compared with contributions from the two- and one-electron interactions. Comparisons with experiment are made.