Relativistic all-order many-body calculations of then=1 andn=2 states of heliumlike ions

An all-order procedure is used to determine the energies of the n=1 and n=2 states of heliumlike ions with nuclear charges in the range Z=3–100. The Coulomb energies and wave functions are obtained from a no-pair Hamiltonian by an iterative scheme that sums all orders of many-body perturbation theory. The Breit energy is determined by taking the expectation value of the instantaneous Breit Hamiltonian between the Coulomb wave functions. Corrections for the frequency dependence of the Breit interaction and for two Breit interactions are included. Quantum-electrodynamic and mass-polarization corrections are taken from Drake’s unified method [Can. J. Phys. 66, 586 (1988)]. The resulting energies are complete through order (Zα${)}^3$ a.u. and include new terms of order (Zα${)}^4$ a.u. Comparisons are made with experiment and with recent configuration-interaction calculations.