Two-loop ladder diagram for the vacuum polarization contribution in hydrogen-like ions

We discuss a calculation scheme for the two-loop ladder graph vacuum polarization contribution to the Lamb shift in hydrogen-like heavy ions. It is obtained by including the vacuum polarization potential self-consistently into the Dirac equation. Numerical values are presented for all systems with nuclear charge numbers . Possible limitations of our method are mentioned. In addition, we also present numerical values for the Wichmann - Kroll contribution to the Lamb shift for all hydrogen-like systems utilizing an extended nuclear charge distribution in the Z-range 30 - 100.