  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.
