Positron emission tomography (PET) is a non-invasive medical imaging technique which provides an image of a positron emitting radio pharmaceutical and its distribution in the body on a metabolic level. At the present time, the performance of this instrument is limited by the nuclear detectors used. One promising approach that has been developed by the researchers at LBL to generate high resolution positron emission tomographs uses a dual detector concept. A photomultiplier tube coupled to several small scintillators is a primary detector for determining the time and the energy of the interaction, while small position sensitive photodetectors attached to the other face of the scintillators identify the crystal that scintillated as well as the depth of interaction. The information from both the detectors is then used to construct a high resolution tomograph. The goal of the proposed Phase I project is to develop a new, fast, high atomic number scintillator, PbSO4, for use in the LBL PET concept. If successful, the use of PbSO4 scintillators in the dual detector approach promises to be the breakthrough needed for the construction of a new generation of high resolution, high rate PET imaging systems.