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With the newly gained interest in the time-of-flight method for positron emission tomography (TOF-PET), many options for pushing the time resolution to its borders have been investigated. As one of these options, the exploitation of the Cherenkov effect has been proposed, since it allows to bypass the scintillation process and therefore provides almost instantaneous response to incident 511 keV annihilation photons. Our simulation studies on the yield of Cherenkov photons, their arrival rate at the photon detector, and their angular distribution reveal a significant influence by Cherenkov photons on the rise time of inorganic scintillators - a key-parameter for TOF in PET. A measurement shows the feasibility to detect Cherenkov photons in this low energy range.