Applicability Limits of the TDCR Method for Non-Pure β Emitters: Case Studies of ²¹⁰Pb and ⁹⁰Sr

The triple-to-double coincidence ratio (TDCR) method is a well-established primary technique for the absolute standardization of pure β-emitting radionuclides in liquid scintillation counting (LSC). Its potential application to radionuclides of dosimetric and environmental relevance characterized by time-dependent decay schemes remains, however, insufficiently explored. This work presents a systematic experimental investigation of the applicability limits and correction strategies required to extend TDCR to non-pure β-emitters, using lead-210 (²¹⁰Pb) and strontium-90 (⁹⁰Sr) as representative and complementary case studies. Measurements were performed using a Hidex 300 SL TDCR system following chemical separation of parent and daughter radionuclides. Direct TDCR-based activity determination yielded statistically consistent results only within a restricted temporal window, corresponding to daughter contributions below approximately 20–22% of the total counting rate. Beyond this interval, TDCR values increased under constant quench conditions, demonstrating sensitivity to changes in the effective β-energy spectrum rather than to quenching effects alone. Activities derived from TDCR measurements were found to follow the temporal evolution predicted by the Bateman formalism, providing a physical basis for implementing a Bateman-based correction. After correction, time-independent parent activities were obtained at any measurement time, with z-scores consistently within statistical acceptance limits. The proposed framework preserves the calibration-standard-free, primary character of TDCR and enables reliable low-level activity determination for radionuclides with complex decay schemes. These results demonstrate that Bateman-corrected TDCR is well suited for early post-intake measurements, routine internal dosimetry, and emergency situations where access to calibration standards is limited or unavailable.