The work presented is part of a design study for a Positron Emission Tomograph (PET) scanner based on the use of BaF2 scintillator and photosensitive wire chambers. The detection efficiency for gamma radiation of 511 keV is found close to 100% for a sufficiently large crystal. For a matrix of small and elongated crystals as one would use in a PET scanner (5 x 5 x 50 mm3) we obtained 6 photoelectrons per 511 keV deposited. The following variants and alternatives were also studied: operation of the wire chamber at atmospheric pressure; double readout where the crystals are read on one side with a photomultiplier to give time and energy resolution, and on the other side with a wire chamber to localise the event; and Csl photocathodes. Encouraging results have been obtained for each of these, but particularly the Csl photocathodes look very promising.