Self-energy radiative corrections in hydrogen-like systems

The one-photon self-energy radiative level shift of an electron in a Coulomb field is examined. An expression for the level shift which is suitable for direct numerical evaluation, for Z in the range 10–110, is obtained. It is based on the known Coulomb radial Green's functions and not on a power series expansion in Zα. In the following paper, the numerical evaluation of the level shift for the $\text{1S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ state is described.