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A combination of analytic and numerical results concerning the instabilities (viz., prompt convection, neutron fingers, and neutrino driven convection) that are suspected of playing an important role in the core collapse supernova mechanism are presented. These results indicate that prompt convection has little effect in triggering an explosion, and that neutron fingers will not develop in the region below the neutrinosphere. A vigorous neutrino driven convection, on the other hand, appears to sufficiently increase the efficiency of neutrino energy deposition behind the shock to power an explosion.
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