Recent Developments for the Investigation of Ground-State Transitions in Heavy One-Electron Ions

Accurate investigations of the structure of one- and few-electron ions in the high-Z regime provide unique possibilities for testing fundamental theories underlaying our present understanding of of the physics of extremely electro-magnetic strong fields. In this review, we concentrate on x-ray spectroscpic investigations of the ground-state transition energies in H-like uranium (heaviest stable element available) by using the intense beams of cooled heavy ions provided by the storage ring ESR at GSI. Such experiments allow for a precise study of the ground-state binding-energies in high-Z H-like ions where relativistic and QED effects are strongest. The most recent experiment is presented where the deceleration capability of the ESR storage ring was exploited for x-ray spectroscopy at the ESR electron cooler. In addition, we discuss the ongoing developments for a new generation of ground-state Lamb shift experiments aiming on a precision of 1 eV or even better. In particular, emphasis will be given to the dedicated crystal spectrometer (FOCAL) in combination with state of the art 2D position-sensitive solid state detectors, allowing for energy and time resolved x-ray imaging.