Stochastic approach of the TDCR model for activity measurement using Cherenkov and liquid scintillation

In the field of radionuclide metrology, the TDCR method is a primary technique based on liquid scintillation using a threephotomultiplier instrumentation. The application of the TDCR model classically implemented in laboratories is investigated in the case of low-energy deposition in the liquid scintillator. For that purpose, the condition of stochastic independence between photomultipliers is introduced in order to express the classical probabilistic relations used for the detection efficiencies of coincidences. Experimentally observed in the case of ³H standardization, the time dependence arises when the coincidence resolving time is shorter than the time distribution of scintillation photons. The geometric dependence is also investigated because of the sensitivity of coincidence counting with the position of light emission inside the volume of the liquid scintillator. For that purpose, a new TDCR modeling using the Monte Carlo code Geant4 has been implemented in order to simulate the propagation of photons from their creation in the optical chamber to the production of photoelectrons in liquid scintillation counter. In both cases of stochastic dependence, the influence on the calculation of detection efficiencies and thus on the activity determination is presented. The new TDCR-Geant4 model was also developed to take into account Cherenkov emission; it has been applied to confirm the emission of Cherenkov photons subsequently created by Compton scattering in the photomultiplier windows. Using the TDCR-Geant4 model, a new primary technique is also presented by implementing the TDCR method using the Cherenkov emission. This new technique has been applied to the standardization of the short-lived radiopharmaceutical ¹¹C (T_1/2 about 20 min).