  We searched for a fast moving H$\alpha$ shell around the Crab nebula. Such a
shell could account for this supernova remnant's missing mass, and carry enough
kinetic energy to make SN 1054 a normal Type II event. Deep H$\alpha$ images
were obtained with WFI at the 2.2m MPG/ESO telescope and with MOSCA at the
2.56m NOT. The data are compared with theoretical expectations derived from
shell models with ballistic gas motion, constant temperature, constant degree
of ionisation and a power law for the density profile. We reach a surface
brightness limit of $5\times10^{-8} ergs s^{-1} cm^{-2} sr^{-1}$. A halo is
detected, but at a much higher surface brightness than our models of
recombination emission and dust scattering predict. Only collisional excitation
of Ly$\beta$ with partial de-excitation to H$\alpha$ could explain such
amplitudes. We show that the halo seen is due to PSF scattering and thus not
related to a real shell. We also investigated the feasibility of a
spectroscopic detection of high-velocity H$\alpha$ gas towards the centre of
the Crab nebula. Modelling of the emission spectra shows that such gas easily
evades detection in the complex spectral environment of the H$\alpha$-line. PSF
scattering significantly contaminates our data, preventing a detection of the
predicted fast shell. A real halo with observed peak flux of about
$2\times10^{-7} ergs s^{-1} cm^{-2} sr^{-1} $ could still be accomodated within
our error bars, but our models predict a factor 4 lower surface brightness. 8m
class telescopes could detect such fluxes unambiguously, provided that a
sufficiently accurate PSF model is available. Finally, we note that PSF
scattering also affects other research areas where faint haloes are searched
for around bright and extended targets.
