Higher order QED binding corrections under special consideration of the self-energy

In this work, higher order QED binding corrections to the self-energy are calculated. It is our aim to determine the non-logarithmic contribution of the order α(Zα)6, which has proven to be a difficult task in the past. This is because due to the two energy scales present in the problem, one has to apply methods of quantum field theory as well as of relativistic atomic physics. These two energy scales are seperated by introducing an overlapping parameter. We present a numerical method where we use a discrete complete basis set on a lattice which allows us to avoid the problems encountered in the previous methods. Therefore, we can calculate this contribution for higher excited states that are important for high-precision spectroscopy but have not been accessible using previous methods