  A simple and computationally efficient parameterization of the
deleptonization, the entropy changes, and the neutrino stress is presented for
numerical simulations of stellar core collapse. The parameterization of the
neutrino physics is based on a bounce profile of the electron fraction as it
results from state-of-the-art collapse simulations with multi-group Boltzmann
neutrino transport in spherical symmetry. Two additional parameters include an
average neutrino escape energy and a neutrino trapping density. The
parameterized simulations reproduce the consequences of the delicate neutrino
thermalization/diffusion process during the collapse phase and provide a by far
more realistic alternative to the adiabatic approximation, which has often been
used in the investigation of the emission of gravitational waves, of
multi-dimensional general relativistic effects, of the evolution of magnetic
fields, or even of the nucleosynthesis in simulations of core collapse and
bounce. For supernova codes that are specifically designed for the postbounce
phase, the parameterization builds a convenient bridge between the point where
the applicability of a stellar evolution code ends and the point where the
postbounce evolution begins.
