Asymmetry of the natural line profile for the hydrogen atom

The asymmetry of the natural line profile for transitions in hydrogen-like atoms is evaluated within a QED framework. For the Lyman-alpha $1s-2p$ absorption transition in neutral hydrogen this asymmetry results in an additional energy shift of 2.929856 Hz. For the $2s_{1/2}-2p_{3/2}$ transition it amounts to -1.512674 Hz. As a new feature this correction turns out to be process dependent. The quoted numbers refer to the Compton-scattering process.