  The method and status of a study to provide numerical, high-precision values
of the self-energy level shift in hydrogen and hydrogen-like ions is described.
Graphs of the self energy in hydrogen-like ions with nuclear charge number
between 20 and 110 are given for a large number of states. The self-energy is
the largest contribution of Quantum Electrodynamics (QED) to the energy levels
of these atomic systems. These results greatly expand the number of levels for
which the self energy is known with a controlled and high precision.
Applications include the adjustment of the Rydberg constant and atomic
calculations that take into account QED effects.
