Description of the ballistic dependance in triple-to-double coincidence ratio (TDCR) method using a surrogate optical...

The Triple-to-Double Coincidence Ratio (TDCR) method is a widely used technique for absolute activity measurements in liquid scintillation counting. While the standard TDCR model assumes statistical independence in photon detection across photomultiplier tubes (PMTs), this study investigates the impact of ballistic dependence, where photon detection probabilities are influenced by the spatial origin of decay events within the scintillator. Using a surrogate bidimensional optical model, the probability distribution of scintillation photon flux among PMTs is sampled and integrated into a Poisson-Multinomial-Binomial hierarchical model of TDCR optics simulation. The results reveal that ballistic dependence leads to a reduction in both double and triple coincidence count rates, causing a corresponding decrease in the TDCR value-particularly for emitters of low energy ionizing radiations such as ⁵⁵Fe or ⁵¹Cr. This effect diminishes with increasing optical diffusion, which effectively decouples photon detection probabilities from the emission site. These results highlight the critical role of maximizing photon diffusion in TDCR counters and underscore the need for refined TDCR models incorporating Monte Carlo-based optical transport to enhance measurement accuracy.