Energy cost that bounce shock wave on its propagation through outer iron core must pay for dissociation of heavy nuclei is considered as an adjusted parameter. Based on this, the method of artificial prompt explosion model is proposed to research effects of iron core mass of SN Ⅱ on prompt explosion. Range of iron core mass of presuperonva models which can produce prompt explosion is estimatd. The preliminary investsgation shows that iron core mass of presupermova models of WW(1993) is too large to produce prompt explosion.

As development of equation of state supernova core collapse will reach high density above nuclear density, the general relativitic effects are most important. The density of core collapse is higher in the general relativitic (GR) core than in the Newtonian (NR) case. The higher the density reached the deeper the shock wave digs into the gravitational well and hance the shock wave will be launched with a larger energy. The formation mass point for shock wave is further from core boundary in GR case than in NR case. The disintegration of iron on the way of shock wave to propagate out will be increased. Once the core centre density reaches it maximum, the imner parts of the cross mass point for two velocity distribution in GR case and in NR case (which slight greater than the sonic mass point in NR case). The velocity value in GR case is greater than one in NR case, but the outer parts of the velocity cross point the velocity value is smaller in GR case than one in NR case, when the shock wave reaches the outer parts where the density and velocity is lower in GR case than in NR, which makes it easier for the shock wave to propagate.

There is a restriction to the solution of the epuation of θ (the ratio between the density of the nuclear matter and the density of the nuclear matter at saturation) in the J. Cooperstein's equ ation of state. Starting from the expression of nucleons pressure near the saturation density at zero temperature, a expression of nucleon internal energy is obtained by us. the re striction mentioned above in J. Cooperstein's equation of state has been removed by substituting the expression of nucleon internal energy obtained by us for the expression used by J.Cooperstein. Me present results of hydrodynamic cal culation of core collapse and subsequent shock wave formation and propagation using the equation of state of us and using the 15M_⊙ initial model of WZW.The relesse of gravitational binding energy of core can be increased by proper softening the equation of state above the sqturation density of nucl ear matter.

The analysis contrasting the feature of BBAL's equation of state (eos) with the feature of equation of state EOS(1) is presental. At range of low density of matter(ρ<10¹¹g cm^-3), the chemical potential of neutron and proton of BBAL's(eos) differs notablly from EOS(1).This results in that two equations of state mentioned above differ greatly in abundance of free neutron and free proton at low density.The difference between the balance expression for finite temperature correct (thermal effect) and for "zero temperature appoximation" has been investegated.The effect for finite temperature correct on the chemical potential of neutron and proton is small, but the effect on the mass number and charge number of the average heavy nucleus is marked.Having taken 15M_① model of weaver et al.as initial model,the collapse process of stellar core between the onset of collapse and core bounce has been calculated by using both the (eos) of BBAL and EOS(1).The results show that the difference betwean the calculational results of stellar collapse (at ρ_c~10¹⁴g cm^-3) with EOS (1) and with BBAL's (eos)is not so large, in spite of that BBAL's (eos) differ greatly from EOS(l) in abundance of free nucleon at low density. The difference between calculational result (at ρ_c~10¹⁴g cm^-3) of stellar collapse resulting from finite temperature correct and "zero temperature approximation" for both BBAL's (eos) and EOS(l) is more notable.