An Approximate Analytic Expression for the Flux Density of Scintillation Light at the Photocathode

The flux density of light exiting scintillator crystals is an important factor affecting the performance of radiation detectors, and is of particular importance for position-sensitive instruments. Recent work by T. Woldemichael developed an analytic expression for the shape of the light spot at the bottom of a single crystal [1]. However, the results are of limited utility because there is generally a light pipe and photomultiplier entrance window between the bottom of the crystal and the photocathode. In this study, we expand Woldemichael's theory to include materials each with different indices of refraction and compare the adjusted light spot shape theory to GEANT 4 simulations [2]. Additionally, light reflection losses from index of refraction changes were also taken into account. We found that the simulations closely agree with the adjusted theory.