Shape of the detected photoelectron spectrum from a scintillating fiber of circular cross-section

The shape of the visible light-photon counter photoelectron spectrum expected from a scintillating fiber of circular cross-section is investigated. Previous work assumed that fibers had uniform thickness and that the spectrum had a Poisson shape. These issues are investigated. Two types of effects are involved in determining the spectrum shape. The first, that ionizing particles traverse different thicknesses in a circular fiber, is geometrical and affects the spectrum in a continuous way. The second effect is stochastic, and results from fluctuations due to various processes. This work combines the two effects in a single illustrative calculation. The resulting photoelectron spectrum is shown not to have a Poisson shape