QED calculation of the interelectron interaction in two- and three-electron ions

Accurate QED evaluations of the one- and two-photon interelectron interaction for the configurations ${1s}_{1/2}{2s}_{1/2}{}^1{S}_0$ and ${1s}_{1/2}{2s}_{1/2}{}^3{S}_1$ in He-like ions and for the configurations ${\mathrm{}\left(1s\right)\mathrm{}}^2{2s}_{1/2}$ and ${\mathrm{}\left(1s\right)\mathrm{}}^2{2p}_{1/2}$ in Li-like ions with nuclear charge numbers $30<~Z<~92$ are performed. The three-photon interaction is also partly taken into account. The QED theory of these corrections is provided by the adiabatic S matrix and by the line-profile approach. The Coulomb gauge is employed. The results are compared with available experimental data and with different calculations.