  We investigate the effects of neutrino heating and alpha-particle
recombination on the hydrodynamics of core-collapse supernovae. Our focus is on
the non-linear dynamics of the shock wave that forms in the collapse, and the
assembly of positive energy material below it. To this end, we perform
time-dependent hydrodynamic simulations with FLASH2.5 in spherical and axial
symmetry. These generalize our previous calculations by allowing for bulk
neutrino heating and for nuclear statistical equilibrium between n, p and
alpha. The heating rate is freely tunable, as is the starting radius of the
shock relative to the recombination radius of alpha-particles. An explosion in
spherical symmetry involves the excitation of an overstable mode, which may be
viewed as the L=0 version of the `Standing Accretion Shock Instability'. In 2D
simulations, non-spherical deformations of the shock are driven by plumes of
material with positive Bernoulli parameter, which are concentrated well outside
the zone of strong neutrino heating. The non-spherical modes of the shock reach
a large amplitude only when the heating rate is also high enough to excite
convection below the shock. The critical heating rate that causes an explosion
depends sensitively on the initial position of the shock relative to the
recombination radius. Weaker heating is required to drive an explosion in 2D
than in 1D, but the difference also depends on the size of the shock. Forcing
the infalling heavy nuclei to break up into n and p below the shock only causes
a slight increase in the critical heating rate, except when the shock starts
out at a large radius. This shows that heating by neutrinos (or some other
mechanism) must play a significant role in pushing the shock far enough out
that recombination heating takes over.
