While in traditional LS counters one or two PMT detectors are integrated, an enhanced counting geometry with three PMTs (120^{0} angles to each other, fig. 7) and two different coincidence outputs has been provided recently (Hidex 300/600 SL, HIDEX). This enables higher counting efficiencies, automated quench correction by triple to double coincidence ratio (TDCR), and luminescence free counting [Haaslahti 2010]. The TDCR method has been originally developed for the direct determination of the absolute activities of β- and EC-decaying radionuclides in liquid scintillator medium. TDCR combines experimental data with theoretical calculations of the detector efficiency. The knowledge of the radionuclide decay scheme data is precondition. A detailed mathematical description on the theory and praxis of TDCR can be found in [Broda 2007], [Nähle and Kossert 2011], [Cassette 2011] and [L’Annunciata 2012].

__Figure 7:__ Instrumentation of Hidex 300 SL TDCR LS counter (Courtesy of HIDEX, Turku)

The sample is measured in all three PMT simultaneously:

The three double coincidence counts (D) AB, BC and CA and the triple coincidence (T) ABC are determined. The ratio of triple to the logical sum of double coincidence counts corresponds to the counting efficiency according to

For pure β-emitters TDCR is directly proportional to the overall efficiency ε. The method allows the activity determination of β-emitters in low and medium quenched samples (both chemical and color quench) without further quench correction.

Deviations of TDCR at higher quench levels (fig. 8) can be eliminated by corrective functions. More recently, the following improved mathematical equation has been presented from core function modelling (CF) for improved counting efficiency calculation using TDCR

Efficiency by CF = [TDCR + a(1-TDCR)^{b}_{*} (9TDCR^{2} / 1+2TDCR)^{2} – TDCR]^{c}

where a, b and c are coefficients depending on radioisotope and cocktail used [Haaslahti et al. 2017]. Fiure 8 presents the DPM values based on TDCR measurement and calculation, and efficiency calculation by CF.

__Figure 8:__ ^{3}H true DPM and values based on calculations, and TDCR calibration vs degree of quenching using nitromethane [Haaslahti et al. 2017]

As has been shown recently the TDCR technique can be extended also to monoenergetic electrons as from electron capture nuclides like ^{55}Fe and ^{41}Ca, as far as the decay scheme is known [Oikari 2012]. The corresponding correction factor is calculated, taking into account the transition probabilities of the Auger-electrons. For photons from γ- and X-ray transitions (^{40}K), their contribution to the electron spectra has to be considered. For the measurement of Cerenkov electrons, their energy spectrum can as well be calculated and used for TDCR calibration. Thus, the TDCR efficiency calculation technique nowadays can be seen as a primary standardization method for radionuclides.

Three PMT detectors, additionally, enable high counting efficiencies with minimum interferences from luminescence (fig. 9). This facilitates the immediate measurement of even high luminescent samples including biooils, without need for dark adaption of samples (see also procedure 2.2.2.1.).

__Figure 9:__ Comparison of spectra by direct detection of bio-oil samples with triple (purple) and double count mode (black; high color luminescence peak); (10 mL oil-samples were mixed 10 mL MaxiLight+ cocktail) [HIDEX 2016]

Portable TDCR counters were developed in recent years at ENEA (Italy), LNHB (France), NPL (UK) and PTB (Germany) in the framework of the European Metrofission project [Cassette et al. 2013]. More recently the design and performance of a portable miniature TDCR counting system with individual extending-type dead-time in each channel has been described [Mitev et al. 2017].

**L’Annunziata M.F. 2012: **“Handbook of Radioactivity Analysis”, Chapter 15, 3^{rd} Edition 2012, Elsevier

**Broda R., Cassette P. and Kossert K. 2007: **Radionuclide metrology using liquid scintillation counting; Metrologia 44 (2007) 36-52

**Cassette P. 2011: **TDCR in a nutshell; in: P. Cassette et.al. “LSC2010 Advances in Liquid Scintillation Spectrometry”, Radiocarbon 2011, Tucson

**Cassette P., Capogni M., Johansson L., Kossert K., Nähle O., Sephton J. and De Felice P. 2013: **Development of portable liquid scintillation counters for on-site primary measurement of radionuclides using the triple-to-double coincidence ratio method; in: Proceedings of the 3^{rd} International Conference on Advancements in Nuclear Instrumentation, Measurement Methods and their Applications (ANIMMA), Marseille, 2013

**Haaslahti V. 2010: **LSC2010 – Hidex, Products for Liquid Scintillation Counting, presented at the International Conference “LSC2010 Advances in Liquid Scintillation Spectrometry”, Paris 2010

**Haaslahti V., Lahdenranta M., Raitanen S., Juvonen R. and Oikari R. 2017: **Improved counting efficiency determination by core function modelling in triple to double coincidence ratio counter; HIDEX Application Note; see also Paper ID 212, “LSC2017 Advances in Liquid Scintillation Spectrometry”, Copenhagen

**HIDEX 2016**: Application Note 413-012, Determination of the ^{14}C content in bio-based products

**Mitev K., Cassette P., Jordanov V., Liu H.R. and Dutsov C. 2017: **Design and performance of a miniature TDCR counting system; J. Radioanal. Nucl. Chem. 314 (2017) 583-589

**Nähle O. and Kossert K. 2011:** Comparison of the TDCR method and the CIEMAT/NIST method for the activity determination of beta emitting nuclides; in: P. Cassette et al. “LSC2010 Advances in Liquid Scintillation Spectrometry”, Radiocarbon 2011, Tucson

**Oikari T. 2012: **TDCR and efficiency for monoenergetic electrons; Technical Note DOC 513-009, HIDEX Oy