While the origin of r -process nuclei remains a long-standing mystery , recent spectroscopic studies of extremely metal-poor stars in the Galactic halo strongly suggest that it is associated with core-collapse supernovae . In this study we examine r -process nucleosynthesis in a “ prompt supernova explosion ” from an 8 - 10 M _ { \odot } progenitor star , as an alternative scenario to the “ neutrino wind ” mechanism , which has also been considered to be a promising site of the r -process . In the present model , the progenitor star has formed an oxygen-neon-magnesium core ( of mass 1.38 M _ { \odot } ) at its center . Its smaller gravitational potential , as well as the smaller core that is in nuclear statistical equilibrium at the time of core bounce , as compared to the iron cores in more massive stars , may allow the star to explode hydrodynamically , rather than by delayed neutrino heating . The core-collapse simulations are performed with a one-dimension , Newtonian hydrodynamic code . We obtain a very weak prompt explosion , in which no r -processing occurs . We further simulate energetic prompt explosions by enhancement of the shock-heating energy , in order to investigate conditions necessary for the production of r -process nuclei in such events . The r -process nucleosynthesis is calculated using a nuclear reaction network code including relevant neutron-rich isotopes with reactions among them . The highly neutronized ejecta ( Y _ { e } \approx 0.14 - 0.20 ) leads to robust production of r -process nuclei ; their relative abundances are in excellent agreement with the solar r -process pattern . Our results suggest that prompt explosions of 8 - 10 M _ { \odot } stars with oxygen-neon-magnesium cores can be a promising site of r -process nuclei . The mass of the r -process material per event is about two orders of magnitude larger than that expected from Galactic chemical evolution studies . We propose , therefore , that only a small fraction of r -process material is ejected , owing to the “ mixing-fallback ” mechanism of the core matter , wherein most of the r -process material falls back onto the proto-neutron star . A lower limit on the age of the universe is derived by application of the U-Th chronometer pair by comparison with the observed ratio of these species in the highly r -process enhanced , extremely metal-poor star CS 31082-001 . The inferred age is 14.1 \pm 2.4 Gyr – the same as that obtained previously based on the neutrino wind scenario with the same nuclear mass formula . This suggests that chronometric estimates obtained using the U-Th pair are independent of the astrophysical conditions considered .