Second-order self-energy-vacuum-polarization contributions to the Lamb shift in highly charged few-electron ions

Proceeding towards the evaluation of the complete set of radiative corrections of order alpha(2) to the energy levels of hydrogenlike systems, the second-order self-energy-vacuum-polarization contribution to the Lamb shift of bound electrons is derived and calculated. We focus on the Uehling part of the vacuum-polarization insertion in the effective photon interaction. Additional energy corrections of order alpha(2) are also calculated. We present a brief summary of various energy contributions for K- and L-shell electrons in hydrogenlike and lithiumlike high-Z ions.