Uncertainties in TDCR measurement revisited: Contribution of optical effects

In the Triple to Double Coincidence Ratio method in Liquid Scintillation Counting, the detection efficiency is calculated from the value of a free parameter describing the intrinsic light yield of the counting system. This model is generally based on a Poisson distribution of the number of photoelectrons detected and the detection efficiency is obtained from the complement of the non-detection efficiency. In the classical free parameter model, the mean of the Poisson distribution, m, is a constant but some variability of this mean could be expected from optical effects due to internal reflections inside the LS source or from non-homogeneity of the detection efficiency of the photomultiplier tubes. Then, m becomes a random variable and the distribution of the photoelectrons becomes a compound Poisson distribution, with a random variable as mean value. This paper explores the implications of the variance of m, which were, to our knowledge, never considered previously in the uncertainty budget of TDCR measurements.