Precise Determination of the Lyman-\(\alpha \)1 Transition Energy in Hydrogen-like Gold Ions with Microcalorimeters

The precise determination of the transition energy of the Lyman-\(\alpha \)1 line in hydrogen-like heavy ions provides a sensitive test of quantum electrodynamics in very strong Coulomb fields. We report the determination of the Lyman-\(\alpha \)1 transition energy of gold ions (Au\(^{78+}\)) with microcalorimeters at the experimental storage ring at GSI. X-rays produced by the interaction of 125 MeV/u Au\(^{79+}\) ions with an internal argon gas-jet target were detected. The detector array consisted of 14 pixels with silicon thermistors and Sn absorbers, for which an energy resolution of 50 eV for an X-ray energy of 59.5 keV was obtained in the laboratory. The Lyman-\(\alpha \)1 transition energy was determined for each pixel in the laboratory frame, then transformed into the emitter frame and averaged. A Dy-159 source was used for energy calibration. The absolute positions of the detector pixels, which are needed for an accurate correction of the Doppler shift, were determined by topographic measurements and by scanning a collimated Am-241 source across the cryostat window. The energy of the Lyman-\(\alpha \)1 line in the emitter frame is \(E(Ly-\alpha 1,Au^{+78})=(71563 \pm 4_{stat} \pm 7_{syst})\) eV, in good agreement with theoretical predictions. The systematic error is dominated by the uncertainty in the position of the cryostat relative to the interaction region of beam and target.