  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.
