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Description
In the Triple to Double Coincidence Ratio (TDCR) 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: if an energy E is transferred to the liquid scintillator, an average of m photoelectrons is detected. The detection efficiency for one photodetector, , is obtained from the complement of the non-detection efficiency, which is the probability to get zero photoelectron when a mean value of m is expected. In the classical free parameter model, m is a constant. Nevertheless, some variability of m could be expected from the following effects:
• With clear LS glass vials, the light emission somewhat depends on its place of emission: the scintillation light has to travel towards the photodetectors, with refractive index steps and, because of internal reflexions, part of the light emitted close to the vial walls could be trapped inside the LS source.
• The photocathode response of the PMTs is not homogeneous, which is due to the variation of its quantum efficiency and photoelectron collection probability.
Then, m becomes a random variable and the distribution of the photoelectrons becomes a compound Poisson distribution, with a random variable as mean value, and characterised by a probability density function depending on the photoelectrons detection process. A preliminary evaluation of the importance of this phenomena can be done by considering the mean value of m, and its associated variance u2(m). The detection efficiency, can still be derived from the non-detection probability by considering the mean value of m, but now, its variance introduces an uncertainty term, where the standard deviation of the detection efficiency is u(m) multiplied by exp(-m). When the number of photoelectrons is large, the exponential term is small and the standard deviation of is negligible. This is not the case when measuring low-energy radionuclides like 3H or 55Fe, and when the detection efficiency of the counter is reduced (e.g., for finding out the optimal value of the kB parameter).
This paper explores the implications of the variance of the free parameter, which were, to our knowledge, never considered previously in the uncertainty budget of TDCR measurements. Three kinds of PMTs are considered: BURLE 8850 and Hamamatsu 7600 and H11934 square tubes. The non-uniformity of these later PMTs, used in miniature TDCR counters, have been experimentally quantified. A Monte Carlo approach is used to evaluate the uncertainty due to photocathode non-homogeneity in the measurement of 3H, 14C, 63Ni and 90Sr by the TDCR method under various counting conditions. Eventually, an evidence of this source of uncertainty is also presented, from the analysis of the experimental standard deviation of the counting rate observed during tritium measurement with reduced detection efficiencies. We demonstrate that the variance of the detection efficiency induces a distortion of the Poisson distribution of the observed disintegration events.
