In a core-collapse supernova event a rapidly rotating neutron star is formed (in the more massive stars this may subsequently collapse to a black hole). Recent studies have indicated that an intrinsic feature of the subsequent explosion is the flood of neutrinos and antineutrinos (of the three flavors) that will heat and transfer momentum to the overlying envelope and expel it. They are also expected to expel a neutron-dominated plasma in a wind from the surface of a simple neutron star lacking rotation and magnetic fields. However, because of the rapid rotation, the magnetic field that connects the neutron star to the overlying envelope should be wrapped into a toroid and the ejected plasma should be incorporated into the accretion disk formed around the star. Simulations of collapsing stellar cores have also shown that rotational flattening will produce a small accretion disk. Such accretion disks in astrophysical objects always appear to form a pair of axial jets. Here the disk plasma should be accelerated out of the disk in the jets with a velocity of the order of 0.5c. The operation of the r-process in this kind of accretion disk and the ejection of the products in the jets has been studied. The critical density in the accretion disk lies in the range 1011-1013 gm cm-3, where nuclear statistical equilibrium (with balance between beta decay and capture) maintains the nuclei well beyond the conventional neutron drip line, with free neutronucleus ratios in the tens to the thousands. The r-process takes place while this material moves toward the base of the jets and beta imbalance allows the proton charge number to increase at a rate of several per second. The plasma coming from the higher densities undergoes fission recycling and produces nuclei mainly at and above A = 132, while the plasma from lower densities produces the lower part of the r-process yields. The jets should also expel material from the still lower density part of the disk in which no r-process has occurred. The interaction of the jets with the surrounding expanding supernova envelope is discussed. Phenomena here involve the spallation formation of the LiBeB elements and the formation of deuterium by similar spallation on helium or by neutron diffusion out of the jets if there is an outer hydrogen region in the expanding envelope. This is probably the origin of the 10Be found as an extinct radioactivity in primitive solar system material, arising from the core-collapse supernova that appears to have triggered the collapse of a molecular cloud core to form the primitive solar nebula, and of the deuterium enhancement at the galactic central region of star formation. The jets constitute a natural way to produce the large variations in abundances detected in the youngest generation of stars. The r-process jets are identified with the gamma-ray bursters as a result of diffusion of gamma rays from the jets, arising from beta decay of the r-process products, and their afterglows are identified with the interactions of the jets in penetrating through the supernova envelopes.
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