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Physics motivation In the future REX-ISOLDE should give the answer to some of the following questions. • Nuclear structure ? How are level schemes, B(El)-values and quadrupole deformations changed in a region close to the drip line? ? What is the most appropriate nuclear model far away from stability? ? Do there exists new regions with extreme nucleus deformation? ? Are there new collective modes to be found with stable octupole, oblate or triaxial nuclear shape? ? Neutron halo nuclei: how many are there and do more forms exist? • Nuclear astrophysics ? The production of primordial matter during the early universe: how did the process continue through the bottlenecks, e.g. through the 35Ar(p,g) reaction? ? What is the magnitude of the astrophysical S factor, and how can the solar neutrino problem be solved? • Atomic physics ? ? Is there a non-parity conservation in heavy ions or atoms? What are the exact masses of short lived medium and heavy isotopes? • Solid state physics ? How will radioactive implantation, creating point defects and impurities, on a deep level in the semiconductor affect its properties? …and much more