S-matrix calculations of energy levels of the lithium isoelectronic sequence*

A QED approach to the calculation of the spectra of the lithium isoelectronic sequence is implemented. A modified Furry representation based on the Kohn-Sham potential is used to evaluate all one- and two-photon diagrams with the exception of the two-loop Lamb shift. Three-photon diagrams are estimated with Hamiltonian methods. After incorporating recent calculations of the two-loop Lamb shift and recoil corrections a comprehensive tabulation of the $2s$, $2p_{1/2}$ and $2p_{3/2}$ energy levels as well as the $2s-2p_{1/2}$ and $2s-2p_{3/2}$ transition energies for $Z=10-100$ is presented.