Evaluation of time measurement precision in the Counting Test Facility of the Borexino experiment

The Counting Test Facility, the prototype of the Borexino experiment installed at the Gran Sasso Laboratory, is an unsegmented liquid scintillator detector in which the spatial reconstruction of the events plays an important role. The event localization is performed through a time of flight technique, which exploits the time informations of the signals of the photomultipliers detecting the photons escaping from the 4 tons scintillation sphere in the center of the detector; thus the uncertainty affecting the time measurement of each anode output represents the ultimate limit on the achievable spatial resolution. This uncertainty has been evaluated by analytical and Monte Carlo calculations based on the actual characteristics of the photomultipliers and of the scintillator adopted for the detector. In this work we present in detail the model assumed to perform the calculations together with the main results obtained. (orig.)