A Generalized Model for Light Transport in Scintillators

Transported light in the medium usually shows as an exponential decay tendency. In the DAMPE strip scintillators, however, the phenomenon of light attenuation as the hit position approaches the end of the scintillator can not be described by the simple exponential decay model. The spread angle of PMT relative to hit position is distance-dependent, so the larger the angle, the larger the proportion $\eta$ of emitted light to becomes the effective input light. We consider the contribution of the spread angle, and propose a generalized model: $f(x)=I_0\eta_{a}(x)e^{-x/\lambda}+I_0\eta_{b}(x)e^{-(2L-x)/\lambda }$. The model well describes the light attenuation in the scintillator, reducing the maximum deviation of the sample from the fit function from 29\% to below 2\%. Moreover, our model contains most of the traditional models, so the experimental data that traditional models can fit and our models fit well.