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

The shape of the visible photon counter (VLPC) photoelectron spectrum expected from a scintillating fiber of circular cross-section is investigated. Two types of phenomena contribute to the spectrum. The first is a continuous effect due to the circular cross-section; the second consists of fluctuations due to various physical processes. For the purpose of a simple illustrative example, only two sources of fluctuation were included: the fluctuation in the number of photons produced by the scintillation, taken to have a Poisson form, and the fluctuation in the binary detection process, which has binomial form. These two types of phenomena were combined by first quantizing the pulse-height spectrum in a way consistent with recent measurements, and then combining the result with the fluctuations. As expected, the calculated VLPC photoelectron spectrum does not exhibit a Poisson shape. Instead, because of the different amounts of light produced by particles traversing different thicknesses in the circular fiber, the distribution is considerably wider relative to its mean.<>