  We present simulation results for a model polymer melt, consisting of short,
nonentangled chains, in the supercooled state. The analysis focuses on the
monomer dynamics, which is monitored by the incoherent intermediate scattering
function. The scattering function is recorded over six decades in time and for
many different wave-vectors. The lowest temperatures studied are slightly above
the critical temperature of mode-coupling theory (MCT), which was determined
from a quantitative analysis of the beta- and alpha-relaxations. We find
evidence for the space-time factorization theorem in the beta-relaxation
regime, and for the time-temperature superposition principle in the
alpha-regime, if the temperature is not too close to the critical temperature.
The wave-vector dependence of the nonergodicity parameter, of the critical
amplitude, and the alpha-relaxation time are in qualitative agreement with
calculations for hard spheres. For wave-vectors larger than the maximum of the
structure factor the alpha-relaxation time already agrees fairly well with the
asymptotic MCT-prediction. The behavior of the relaxation time at small
wave-vectors can be rationalized by the validity of the Gaussian approximation
and the value of the Kohlrausch stretching exponent.
