Radiative corrections to the energy levels of "murium," an electron bound by its image charge to a wall

Radiative corrections generate shifts in the Rydberg levels of "murium," the system composed of an electron bound by its image charge to a plane wall, which are proportional to the fine structure constant $\alpha$; if the wall is perfectly conducting and impenetrable the shift in the ground-state energy is 0.2%, extraordinarily large for a radiative correction. (The difference from the usual hydrogenic Lamb shift, which goes roughly as ${\alpha }^3$, originates in the fact that the vacuum fluctuation fields near the wall differ from those in free space, so that on renormalization the leading terms are not completely canceled.) The absolute shift is greatly reduced for a realistic wall.