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Precision spectroscopy on simple and complex atomic ions in traps

We discuss the Ca+ ion as a "simple" atomic system, described as an electronic three-level system. In a Paul ion trap a small ion cloud can be laser cooled until crystallisation appears which reduces the ion motion. Lifetime and hyperfine structure measurements in ground and excited electronic states can be performed with high precision. A first example for the investigation of a "complex" ionic system is represented by the Eu+ ion, where hyperfine structure splittings have been obtained with uncertainties in the 10−9 range even on radioactive isotopes with few available particles. These small uncertainties require extensive and complicated pertubation calculation for a determination of coupling constant, but open the way for detailed investigation of nuclear structure effects.