Abstract: Large accelerators with radioactive beams presently under construction will allow the synthesis and the investigation of new rare isotopes in the laboratory. So far, these nuclei exist only for short times in astrophysical environments such as supernova explosions and explosive nuclear burnings. They are crucial for the genesis of all the heavy elements in our universe and our live on earth. Theoretical methods will be discussed, which allow the description of the presently know and the prediction of such isotopes far from the valley of stability. New phenomena, such as proton radioactivity, neutron skins and halo's and the synthesis of super-heavy elements can be understood in this way.

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