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During iron core collapse and subsequent neutron star formation in massive stars, $\sim 10$\% of the binding energy of the neutron star is released during a Kelvin-Helmholtz time scale in the form of neutrinos whose energy is depositied within an atmosphere in near hydrostatic equilibrium, giving rise to a ``neutrino-driven wind''. This wind is powered by neutrino/antineutrino capture on nucleons which, due to to hardening of the antineutrino spectrum at late times, causes the material to become neutron-rich. Additionally, due to the short pressure scale height, the region will have a high entropy ($30 \le S/N_Ak \le 450$). These conditions conspire to form a region that is especially well suited to the production of the $r$-process. We present calculations that study the detailed nucleosynthesis that occurs within the last 0.02 M$_{\sun}$ of material ejected in the delayed explosion of a 20 M$_{\sun}$ Type II supernova model. The thermal and compositional evolution of a large number of sample trajectories (40 choices of $\rho (t), T(t), Y_e(t)$) that decrease smoothly and logarithmically down to $10^{-6}$ M$_{\sun}$ are followed for times as late as 15 seconds after core collapse. We find that a large number of isotopes from mass A$\sim 60$ to 200 are produced in quantities of interest to galactic chemical evolution.
Unfortunately, the model does not give a satsifactory $r$-process. The two basic problems are too much material having entropy $\sim 40$ and $Y_e \le 0.47$ which comprises much of the ejecta at times in the evolution of the wind before the conditions for the $r$-process are acheived. These conditions consipre to overproduce nuclei in the $N=50$ closed neutron shell to such a degree that the star is incapable of producing even oxygen. Additionally, the entropy at late times needs to be $\approx 50$\% larger to produce the heaviest $r$-process isotopes. In an acceptable model the entropy would be lower at early times when the mass loss rate is large and higher at late times when the mass loss rate is small. Reasons for why this might actually occur in nature are discussed. Despite the current difficulties found in this particular model, neutrino powered winds from nacent neutron stars remain very attractive sites for the $r-$process.
