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Atomic nuclei are held together by the strong interaction between neutrons and protons. About ten percent of all known nuclei are stable. Starting from these stable isotopes, nuclei become increasingly unstable as neutrons are added or removed, until neutrons can no longer bind to the nucleus and drip out. This limit of existence, the so-called neutron dripline , has so far been discovered experimentally only for light elements up to neon. Understanding the neutron dripline and the structure of neutron-rich nuclei also plays a key role in the research program for the future accelerator facility FAIR at the GSI Helmholtz Centre for Heavy Ion Research in Darmstadt.