$S$-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.

Figure 1

One-photon correlation and radiative diagrams. A cross inside a circle represents a counterpotential.

Figure 2

Two-photon correlation diagrams. A cross inside a circle represents a counterpotential.

Figure 3

Screened vacuum polarization diagrams. A cross inside a circle represents a counterpotential.

Figure 4

Screened self-energy diagrams. A cross inside a circle represents a counterpotential.

Figure 5

Structure energies (eV) of the $2s–2p_{1/2}$ transition relative to the present results. Solid squares, Blundell [25]; solid circles, RCI [30]; dotted line, St. Petersburg group [32].

Figure 6

Structure energies (eV) of the $2s–2p_{3/2}$ transition relative to the present results. Solid squares, Blundell [25]; solid circles, RCI [30]; dotted line, St. Petersburg group [32].

Figure 7

Screened QED energies (eV) of the $2s–2p_{1/2}$ transition relative to the present results. Solid squares, Blundell; solid circles, RCI; open circles, RCI relaxed QED; open triangles, St. Petersburg group. See Table for references.

Figure 8

Screened QED energies (eV) of the $2s–2p_{3/2}$ transition relative to the present results. Solid squares, Blundell; solid circles, RCI; open circles, RCI relaxed QED; open triangles, St. Petersburg group. See Table for references.

Figure 9

The $2s–2p_{1/2}$ transition energies (eV) relative to the present results. Solid squares, Blundell; solid circles, RCI; open triangles, St. Petersburg group; crosses, experiment. See Table for references.

Figure 10

The $2s–2p_{3/2}$ transition energies (eV) relative to the present results. Solid squares, Blundell; solid circles, RCI; open circles, RCI with relaxed QED; open triangles, St. Petersburg group; crosses, experiment. See Table for references.