The high scintillation luminosity of n-type GaAs at 10 °K is surprising because (1) with a refractive index of 3.5, escape is inhibited by total internal reflection and (2) narrow-beam experiments at 90 °K report infrared absorption coefficients of several per cm. This paper presents Monte Carlo calculations showing that the high luminosity at 10 °K can be explained if (1) the narrow-beam absorption is almost all optical scattering and (2) the absolute absorption coefficient is below 0.1 per cm. Sixteen surface reflector configurations are simulated for a range of internal scattering and absolute absorption coefficients, and these can guide the design of cryogenic scintillating GaAs targets for the direct detection of dark matter. The discussion section presents a possible infrared scattering mechanism based on the metallic nature of n-type GaAs. A supplement file describes (1) the Monte Carlo program steps in detail and (2) how narrow-beam and integrating sphere experiments can measure the cryogenic optical scattering and absolute absorption coefficients.

This paper demonstrates through Monte Carlo simulations that a practical positron emission tomograph with (1) deep scintillators for efficient detection, (2) double-ended readout for depth-of-interaction information, (3) fixed-level analog triggering, and (4) accurate calibration and timing data corrections can achieve a coincidence resolving time (CRT) that is not far above the statistical lower bound. One Monte Carlo algorithm simulates a calibration procedure that uses data from a positron point source. Annihilation events with an interaction near the entrance surface of one scintillator are selected, and data from the two photodetectors on the other scintillator provide depth-dependent timing corrections. Another Monte Carlo algorithm simulates normal operation using these corrections and determines the CRT. A third Monte Carlo algorithm determines the CRT statistical lower bound by generating a series of random interaction depths, and for each interaction a set of random photoelectron times for each of the two photodetectors. The most likely interaction times are determined by shifting the depth-dependent probability density function to maximize the joint likelihood for all the photoelectron times in each set. Example calculations are tabulated for different numbers of photoelectrons and photodetector time jitters for three 3  ×  3  ×  30 mm³ scintillators: Lu₂SiO₅:Ce,Ca (LSO), LaBr₃:Ce, and a hypothetical ultra-fast scintillator. To isolate the factors that depend on the scintillator length and the ability to estimate the DOI, CRT values are tabulated for perfect scintillator-photodetectors. For LSO with 4000 photoelectrons and single photoelectron time jitter of the photodetector J  =  0.2 ns (FWHM), the CRT value using the statistically weighted average of corrected trigger times is 0.098 ns FWHM and the statistical lower bound is 0.091 ns FWHM. For LaBr₃:Ce with 8000 photoelectrons and J  =  0.2 ns FWHM, the CRT values are 0.070 and 0.063 ns FWHM, respectively. For the ultra-fast scintillator with 1 ns decay time, 4000 photoelectrons, and J  =  0.2 ns FWHM, the CRT values are 0.021 and 0.017 ns FWHM, respectively. The examples also show that calibration and correction for depth-dependent variations in pulse height and in annihilation and optical photon transit times are necessary to achieve these CRT values.