The accurate determination of the Lamb shift in heavy hydrogen-like ions provides a sensitive test of quantum electrodynamics in very strong Coulomb fields, not accessible otherwise. For the investigation of the Lyman-a transitions in ~(208)Pb~(81+) or ~(238)U~(91+) with sufficient accuracy, a high resolution calo-rimetric detector for hard x-rays (E ≤ 100 keV) is presently being developed. The detector modules consist of arrays of silicon thermistors and of x-ray absorbers made of high-Z material to optimize the absorption efficiency. The detectors are housed in a specially designed ~3He/~4He dilution refrigerator with a side arm which fits to the internal target geometry of the storage ring ESR at GSI Darmstadt. The detector performance presently achieved is already close to fulfill the demands of the Lamb shift experiment. For a prototype detector pixel with a 0.2 mm~2 X 47 μm Pb absorber an energy resolution of ΔE_(FWHM) = 65 eV is obtained for 60 keV x-rays.
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