Time and position distributions in large volume spherical scintillation detectors

Large spherical scintillation detectors are playing an increasingly important role in experimental neutrino physics studies. From the instrumental point of view the primary signal response of these set-ups is constituted by the time and amplitude of the anode pulses delivered by each individual phototube following a particle interaction in the scintillator. In this work, under some approximate assumptions, we derive a number of analytical formulas able to give a fairly accurate description of the most important timing features of these detectors, intended to complement the more complete Monte Carlo studies normally used for a full modelling approach. The paper is completed with a mathematical description of the event position distributions which can be inferred, through some inference algorithm, starting from the primary time measures of the photomultiplier tubes.