  We revisit potential impacts of nuclear burning on the onset of the
neutrino-driven explosions of core-collapse supernovae. By changing the
neutrino luminosity and its decay time to obtain parametric explosions in
one-(1D) and two-dimensional (2D) models with or without a 13-isotope alpha
network, we study how the inclusion of nuclear burning could affect the
postbounce dynamics for four progenitor models; three for 15.0 Msun stars, one
for an 11.2 Msun star. We find that the energy supply due to nuclear burning of
infalling material behind the shock can energize the shock expansion especially
for models that produce only marginal explosions in the absence of nuclear
burning. These models are energized by nuclear energy deposition when the shock
front passes through the silicon-rich layer and/or later it touches the
oxygen-rich layer. Depending on the neutrino luminosity and its decay time, a
diagnostic energy of explosion increases up to a few times 10^50 erg for models
with nuclear burning compared to the corresponding models without. We point out
that these features are most remarkable for the Limongi-Chieffi progenitor in
both 1D and 2D, because the progenitor model possesses a massive oxygen layer
with its inner-edge radius being smallest among the employed progenitors, so
that the shock can touch the rich fuel on a shorter timescale after bounce. The
energy difference is generally smaller (~0.1-0.2 times 10^51 erg) in 2D than in
1D (at most ~0.6 times 10^51 erg). This is because neutrino-driven convection
and the shock instability in 2D models enhance the neutrino heating efficiency,
which makes the contribution of nuclear burning relatively smaller compared to
1D models. Considering uncertainties in progenitor models, our results indicate
that nuclear burning should remain as one of the important ingredients to
foster the onset of neutrino-driven explosions.
