We present a spherically symmetric , Newtonian core-collapse simulation of a 15 M _ { \odot } star with a 1.28 M _ { \odot } iron core .
The time- , energy- , and angle-dependent transport of electron neutrinos ( \nu _ { e } ) and antineutrinos ( \bar { \nu } _ { e } ) 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 \sim 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 \sim 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 M _ { \odot } 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 A \approx 90 in exploding models may be absent when a Boltzmann solver is used for the \nu _ { e } and \bar { \nu } _ { e } transport .