  We present a spherically symmetric, Newtonian core-collapse simulation of a
15 solar mass star with a 1.28 solar mass iron core. The time-, energy-, and
angle-dependent transport of electron neutrinos and antineutrinos was treated
with a new code which iteratively solves the Boltzmann equation and the
equations for neutrino number, energy and momentum to order O(v/c) in the
velocity v of the stellar medium. The supernova shock expands to a maximum
radius of 350 km instead of only about 240 km as in a comparable calculation
with multi-group flux-limited diffusion (MGFLD) by Bruenn, Mezzacappa, & Dineva
(1995). This may be explained by stronger neutrino heating due to the more
accurate transport in our model. Nevertheless, after 180 ms of expansion the
shock finally recedes to a radius around 250 km (compared to about 170 km in
the MGFLD run). The effect of an accurate neutrino transport is helpful, but
not large enough to cause an explosion of the considered 15 solar mass star.
Therefore postshock convection and/or an enhancement of the core neutrino
luminosity by convection or reduced neutrino opacities in the neutron star seem
necessary for neutrino-driven explosions of such stars. We find an electron
fraction Y_e > 0.5 in the neutrino-heated matter, which suggests that the
overproduction problem of neutron-rich nuclei with mass numbers around A = 90
in exploding models may be absent when a Boltzmann solver is used for the
electron neutrino and antineutrino transport.
