Time and space reconstruction in optical, non-imaging,   scintillator-based particle detectors
  A new generation of ultra-low-background scintillator-based detectors aims to study solar neutrinos and search for dark matter and new physics beyond the Standard Model. These optical, non-imaging detectors generally contain a "fiducial volume" from which data are accepted, and an "active buffer region" where there are higher levels of radioactive contaminants. Events are observed in real time. To distinguish between events occurring in the two regions, it is imperative that event position reconstruction be well-understood. 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 delta a ~ (c sigma / n) sqrt(3/N), where sigma 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, 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. 
Cristiano Galbiati and Kevin McCarty