The identification of the astrophysical site and the specific conditions in which r-process nucleosynthesis takes place remain unsolved mysteries of astrophysics. The present paper emphasizes some important future challenges faced by nuclear physics in this problem, particularly in the determination of the radiative neutron capture rates by exotic nuclei close to the neutron drip line and the fission probabilities of heavy neutron-rich nuclei. These quantities are particularly relevant to determine the composition of the matter resulting from the decompression of initially cold neutron star matter. New detailed r-process calculations are performed and the final composition of ejected inner and outer neutron star crust material is estimated. We discuss the impact of the many uncertainties in the astrophysics and nuclear physics on the final composition of the ejected matter. The similarity between the predicted and the solar abundance pattern for A > 140 nuclei as well as the robustness of the prediction with varied input parameters makes this scenario one of the most promising that deserves further exploration.
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