  We explore the diffractive interaction of a proton with an anti-proton which
results in centrally produced dijets. This process has been recently studied at
the Tevatron. We make predictions within an Ingelman-Schlein approach and
compare them to the recent data presented by the CDF collaboration. Earlier
calculations resulted in theoretical cross-sections which are much larger than
those observed by CDF. We find that, after consideration of hadronisation
effects and the parton shower, and using parton density functions extracted
from diffractive deep inelastic scattering at HERA, it is possible to explain
the CDF data. We need to assume a gap survival probability of around 10% and
this is in good agreement with the value predicted by theory. We also find that
the non-diffractive contribution to the process is probably significant in the
kinematical region probed by the Tevatron.
