  The high scintillation luminosity of n-type GaAs at 10K is surprising because
(1) with a refractive index of about 3.5, escape is inhibited by total internal
reflection and (2) narrow-beam experiments at 90K report infrared absorption
coefficients of several per cm. This paper presents Monte Carlo calculations
showing that the high luminosity at 10K can be explained if (1) 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. Appendix A describes the Monte Carlo program steps in detail.
Appendix B shows how narrow-beam and integrating sphere experiments can measure
the cryogenic optical scattering and absolute absorption coefficients.
