Complete Single$-$Center Basis Sets in Atomic Calculations*

Single particle orbitals centered on the nucleus are the most commonly used basis in large-scale calculations of atomic structure. The convergence towards a complete basis set, with respect to both the number and angular momenta of the orbitals included in a configuration interaction (CI) expansion, has been investigated using the ground and excited states of the helium atom [1,2,3]. This enabled energies to be determined to within $10^{-8}$ Hartree, whilst the convergence of the electron-electron $\delta$-function and other relativistic corrections have been examined in detail. Unusual convergence patterns in the CI-Kohn variational scattering method have been observed and, however, high-precision calculations of elastic positron scattering from atoms are achievable [4].\\ $[1]$ J.Mitroy, M.W.J.Bromley, K.Ratnavelu Int.J.Quant.Chem. \textbf{107} 907 (2007). \\ $[2]$ M.W.J.Bromley and J.Mitroy Int.J.Quant.Chem. \textbf{107} 1150 (2007). \\ $[3]$ K.Rollin, M.W.J.Bromley and J.Mitroy (in preparation). \\ $[4]$ S.I.Young, M.W.J.Bromley and J.Mitroy (in preparation).