  We consider the single particle correlations and momentum distributions in a
gas of strongly interacting spinless 1D fermions with zero-range interactions.
This system represents a fermionic version of the Tonks-Girardeau gas of
impenetrable bosons as it can be mapped to a system of noninteracting 1D
bosons. We use this duality to show that the T=0 single particle correlations
exhibit an exponential decay with distance. This strongly interacting system is
experimentally accessible using ultracold atoms and has a Lorentzian momentum
distribution at large momentum whose width is given by the linear density.
