Time and space reconstruction in optical, non-imaging, scintillator-based particle detectors

A new generation of ultra-low-background, non-imaging scintillator detectors is being developed to study solar neutrinos and search for dark matter. These detectors generally contain a "fiducial volume," where the signal to noise ratio is maximal, surrounded by an "active buffer region." To distinguish between events occurring in the two regions, the position of each event in space and time is reconstructed starting from the spatial and temporal distribution of the photons collected. The object of this paper is the study of the reconstruction, in time and space, of scintillation events in detectors of large dimensions. A general, likelihood-based method of position reconstruction for this class of detectors is presented. The potential spatial resolution of the method is then evaluated. It is shown that for a spherical detector with a large number N of photosensitive elements that detect photons, the expected spatial resolution at the center of the detector is given by δ a ≈ (c σ / n) sqrt(3 / N), where σ is the width of the scintillator time response function and n is the index of refraction in the medium. However, if light in the detector has a scattering mean free path much less than the detector radius R, so that the information on the time of detection of the photons becomes irrelevant, and only the spatial distribution of the detected photons is of essence, the resolution instead becomes (R / 2) sqrt(3 / N). Finally, a formalism is introduced to deal with the common case in which only the arrival time of the first photon to arrive at each photosensitive element can be measured.