We conducted one-dimensional and two-dimensional hydrodynamic simulations of post-shock revival evolutions in core-collapse supernovae, employing the simple neutrino light bulb approximation to produce explosions rather easily. In order to estimate the explosion energy, we took into proper account nuclear recombinations and fusions consistently with the equation of state for matter not in statistical equilibrium in general. The methodology is similar to our previous work, but is somehow improved. In this paper, we studied the influence of the progenitor structure on the dynamics systematically. In order to expedite our understanding of the systematics, we constructed six parametric progenitor models, which are different in masses of Fe iron core and Si+S layer, instead of employing realistic models provided by stellar evolution calculations, which are sometimes of stochastic nature as a function of stellar mass on the main sequence. We found that the explosion energy is tightly correlated with the mass accretion rate at shock revival irrespective of dimension and the progenitors with light iron cores but with rather high entropies, which have yet to be produced by realistic stellar evolution calculations, may reproduce the canonical values of explosion energy and nickel mass. The mass of the Si+S layer is also important in the mass accretion history after bounce, on the other hand; the higher mass accretion rates and resultant heavier cores tend to hamper strong explosions.
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