Current numerical simulations of the collapse of the iron cores of massive stars indicate that the bounce of the imploding matter at around nuclear densities and the subsequent shock wave are not energetic enough to eject the envelope and yield a Type II supernova. The culprit is predominantly the nuclear dissociation of the mantle, which saps the shock of thermal energy and hence pressure. Conditions are obtained which are necessary for the shock energy to exceed the dissociation energy (plus neutrino losses), i.e., for stellar collapse to lead to a supernova. In simple terms either a small initial core or a large trapped lepton fraction (YL) is required. The only reasonable way to guarantee a large YL is for the initial entropy (S) of the core to be relatively small. The critical value of the entropy is derived as a function of the initial core size. For a large core (1.5 solar mass), S must be less than 0.5; a small core (1.2 solar mass) still requires S to be less than 1. It is shown that uncertainties in the equation of state are not likely to alter results.
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Burrows et al. (1983) studied this question.