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

Energies of the 4s1/2, 4p1/2 and 4p3/2 states of Cu-like ions with nuclear charges in the range Z=29-92 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≥50, and that omitted correlation contributions to the 4p3/2-4s1/2 energy intervals are less than the numerical errors for Z≥35. The theoretical 4p3/2-4s1/2 energy intervals, and the 4p3/2-4p1/2 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 $n=4$ Lamb shift.