  The spectral-weight distribution in recent neutron scattering experiments on
the parent compound La$_2$CuO$_4$ (LCO), which are limited in energy range to
about 450\,meV, is studied in the framework of the Hubbard model on the square
lattice. We find that the higher-energy weight extends to about 566\,meV and is
located at and near the momentum $[\pi,\pi]$. Our results confirm that the
$U/t$ value suitable to LCO is in the range $U/t\in (6,8)$. The continuum
weight energy-integrated intensity vanishes or is extremely small at momentum
$[\pi,0]$. This behavior of the intensity is consistent with that of spin
waves, which are damped at $[\pi,0]$.
