All-order relativistic many-body calculations for the electron affinities of ${\mathrm{Ca}}^{\mathrm{-}}$, ${\mathrm{Sr}}^{\mathrm{-}}$, ${\mathrm{Ba}}^{\mathrm{-}}$, and ${\mathrm{Yb}}^{\mathrm{-}}$ negative ions

Electron affinities are evaluated for negative ions formed by the attachment of one electron to atoms with closed subshells, using relativistic many-body perturbation theory. In particular, we investigate the ${\mathrm{Ca}}^{\mathrm{-}}$, ${\mathrm{Sr}}^{\mathrm{-}}$, ${\mathrm{Ba}}^{\mathrm{-}}$, and ${\mathrm{Yb}}^{\mathrm{-}}$ ions. Starting from a model space that consists of nondegenerate valence Dirac-Hartree-Fock orbitals, we first approximate the energy of the attached electron as the lowest eigenvalue of a second-order effective Hamiltonian. Higher-order correlation corrections are calculated in the linear cluster approximation. The Breit interaction is also included in the first order. Our results are in good agreement with recent experiments and show a clear improvement over the second-order Dyson equation. Comparisons with other many-body calculations are also presented.