Monte Carlo uncertainty propagation in efficiency calculations for 4πγ counting of 134 Cs and 137 Cs

Abstract 4πγ counting is an important method for radionuclide activity standardization, with relatively simple source preparation and experimental operation. However, its accuracy depends strongly on the calculated nuclide-specific total detection efficiency. The efficiency calculation involves numerous input quantities, including detector dimensions, material properties, source geometry, nuclear decay data, photon interaction cross sections, and energy threshold. A comprehensive evaluation of the uncertainties associated with these inputs therefore remains challenging. Detailed particle-transport simulations provide considerable flexibility in efficiency calculations, but become computationally intensive when embedded in a Monte Carlo uncertainty propagation procedure. In this study, the framework described in Supplement 1 to the Guide to the Expression of Uncertainty in Measurement was implemented for 4πγ counting using a custom-built well-type NaI(Tl) detector. The principal input uncertainties were propagated through detailed particle-transport simulations based on a Geant4 model for 134 Cs and 137 Cs. The convergence of the estimated efficiency uncertainty with the number of trials was examined, and 4000 trials were adopted for each calculation. The relative standard uncertainties of the calculated total detection efficiencies were 0.15% and 0.64% for 134 Cs and 137 Cs, respectively. Activity concentrations determined by 4πγ counting agreed with independent results obtained by 4πβ(PC)–γ coincidence counting and efficiency tracing. This implementation provides a practical means of evaluating detection-efficiency uncertainty in 4πγ counting based on detailed particle-transport simulations.