Evaluation of the accidental coincidence counting rates in TDCR counting

This paper presents analytical and experimental methods to evaluate the accidental coincidence counting rates in a Triple-to-Double Coincidence Ratio (TDCR) Liquid Scintillation (LS) measurement.

The experimental method we propose is based on the analysis of the distribution of the time delays between the first detected events in each photomultiplier tube. The underlying assumption is that events separated by several microseconds in time are not correlated, thus the accidental coincidence counting rates could be determined from the time interval distribution of uncorrelated events. The analytical evaluation of the accidental coincidence counting rates is based on the conditional probabilities for the occurrence of uncorrelated events within the same coincidence resolving time. The analytical and experimental evaluations of the rate of accidental coincidences give consistent results for TDCR measurements of $^{3}$H, $^{55}$Fe and $^{14}$C. The two methods were used to evaluate corrections for accidental coincidences for Monte Carlo (MC) generated list-mode files of $^{3}$H measurements with increasing activities. The counting rates, corrected for accidental coincidences using the analytical method, are within 0.29% of the MC reference up to 100 kBq and the corrected, using the experimental method, are within 0.21% up to 200 kBq.