Many-body perturbation-theory calculations of energy levels along the copper isoelectronic sequence

Energies of the $4s_{\frac{1}{2}}$, $4p_{\frac{1}{2}}$ and $4p_{\frac{3}{2}}$ states of Cu-like ions with nuclear charges in the range $Z=29-92\mathrm{}$ are calculated using relativistic many-body perturbation theory. These calculations include the lowest-order Dirac-Fock energies, second- and third-order Coulomb correlation corrections, the lowest-order retarded Breit interaction, second- and third-order correlation corrections to the Breit interaction, finite nuclear size corrections, and corrections for reduced mass and mass polarization. The order of magnitude of the omitted fourth- and higher-order correlation corrections is estimated by chaining second-order Brueckner orbitals. Using this estimate, we find that omitted correlation corrections to the ionization energies are less than the numerical error in the terms included in the calculation for $Z\ge 50$, and that omitted correlation contributions to the $4p_{\frac{3}{2}}-4s_{\frac{1}{2}}$ energy intervals are less than the numerical errors for $Z\ge 35$. The theoretical $4p_{\frac{3}{2}}-4s_{\frac{1}{2}}$ energy intervals, and the $4p_{\frac{3}{2}}-4p_{\frac{1}{2}}$ fine-structure intervals are compared with experiment to determine the QED contributions to the energies. The QED corrections inferred in this way are accounted for approximately by semiempirical values of the $n=4\mathrm{}$ Lamb shift.