  We present a range of steady-state photoionization simulations, corresponding
to different assumed shell geometries and compositions, of the unseen
postulated rapidly expanding outer shell to the Crab Nebula. The properties of
the shell are constrained by the mass that must lie within it, and by limits to
the intensities of hydrogen recombination lines. In all cases the
photoionization models predict very strong emission from high ionization lines
that will not be emitted by the Crab's filaments, alleviating problems with
detecting these lines in the presence of light scattered from brighter parts of
the Crab. The NIR [Ne VI] $\lambda$7.652 $\mu$m line is a particularly good
case; it should be dramatically brighter than the optical lines commonly used
in searches. The C IV $\lambda1549\AA$ doublet is predicted to be the strongest
absorption line from the shell, which is in agreement with HST observations. We
show that the cooling timescale for the outer shell is much longer than the age
of the Crab, due to the low density. This means that the temperature of the
shell will actually "remember" its initial conditions. However, the
recombination time is much shorter than the age of the Crab, so the predicted
level of ionization should approximate the real ionization. In any case, it is
clear that IR observations present the best opportunity to detect the outer
shell and so guide future models that will constrain early events in the
original explosion.
