The fast scintillation decay time and the high scintillation yield of liquid xenon makes it an appropriate material for nuclear medicine. Moreover, being a continuous medium with a uniform response, liquid xenon allows one to avoid most of the geometrical distortions of conventional detectors based on scintillating crystals. In this paper, we describe how these properties have motivated the development of a novel concept for positron emission tomography scanners with Time-Of-Flight measurement, which uses liquid xenon as a scintillating material and silicon photomultipliers as sensors. Monte Carlo studies have indicated that this technology would provide a very good intrinsic time resolution, of around 70 ps. Moreover, being liquid xenon transparent to UV and blue wavelengths, both scintillation and Cherenkov light can be exploited. While the former can be used for energy measurements, the latter is a prompt signal (of a few picoseconds), which provides a very precise time measurement. Monte Carlo simulations point to a time resolution of 30-50 ps obtained using Cherenkov light. A first prototype is being built to demonstrate the high energy, spatial and time resolution of this concept, using a ring of around 30 cm of internal diameter and a depth of 3 cm instrumented with VUV--sensitive silicon photomultipliers.
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