  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.
