Explosive nucleosynthesis and the astrophysical r-process

We give an overview of chemical equilibria in explosive burning and the role which neutron and/or proton separation energies play. We focus then on the rapid neutron-capture process (r-process) which encounters unstable nuclei far from beta-stability with neutron separation energies in the range 1-4 MeV. Its observable features, like the abundances, witness nuclear structure as well as the conditions in the appropriate astrophysical environment. With the remaining lack of a full understanding of its astrophysical origin, parametrized calculations are still necessary. The classical approach is based on (constant) neutron number densities n(n) and temperatures T over duration timescales tau. Recent investigations, motivated by the neutrino wind scenario from hot neutron stars after a supernova explosion, followed the expansion of matter with initial entropies S and electron fractions Y-e over expansion timescales tau. We compare the similarities and differences between the two approaches with respect to resulting abundance features and their relation to solar r-process abundances. Special emphasis is given to the questions (i) whether the same nuclear properties far from stability lead to similar abundance patterns and deficiencies in both approaches and (ii) whether some features can also provide clear constraints on the permitted astrophysical conditions.