The detection unit of 3PM-γ coincidence system installed at Mokwon University is shown in Fig. 1. Three photo-detectors used for β-detectors are the PM tubes of Hamamatsu R1847-07 with bi-alkali photocathode of 51 mm in diameter. These β-detectors in the plane were designed to move back and forth from centrally located liquid scintillation vial by a connecting gear. A vise ties up them to move at a same time manually up to 50 mm by rotating a saw-toothed gear. Another three photon detectors, NaI(Tl), HPGe, and X-ray detector, are located 120 mm rear from the front of β-detectors not to screen the scintillation pulses incident on the windows. In the present work, a NaI(Tl) detector, 254 mm (long)×251 mm (diameter) was used in the γ-counting channel. Detection unit is located in a cylindrical chamber of 650 mm in inner diameter and 320 mm high and the outer wall is shielded by a 20-mm thick lead plate.

The dynode outputs of each PM tube in the β-channel is amplified and converted to a positive transistor-transistor logic (TTL) signal with 500 ns width at single channel analyzer (SCA). Thermal noises could be rejected at coincidence channels, so the threshold level of each γ-counting channel was lowest level +60 mV of applied SCA. Three double coincident events from these signals are analyzed and their logical sum N_D is obtained (N_D becomes β-events). The resolving time was 500 ns, the width of the SCA output signal. Both the SCA output N_γ from γ-channel and the N_D are input to Pulse Gate, custom-made at the factory for this work. It was fabricated in an integrated circuit so that it not only adjusts the delay time and pulse width of each output pulse, but also has the ability to do AND/OR works. All operations are controlled by the RSC 232 serial communication port. Delay time and pulse width, whichever is longer, becomes the dead time of corresponding counting channel. It is non-extending type. Outputs from Pulse Gate, N_D, N_γ and coincidence counting N_Dγ, are recorded in Data Acquisition device. The simplified block diagram of the applied electronics is displayed Fig. 2. The modules laying inside rectangular box are logic signal analyzers specially designed for this work.

Liquid scintillation samples were prepared by mixing aliquots of a radioactive solution of ¹³⁴Cs with 10 mL liquid scintillator. It was same one used at our earlier work [2]. This radionuclide is very important for calibration of γ-ray spectrometry and also used as a tracer for ¹³⁷Cs activity determination [9, 10]. It decays mainly by β-emission to ¹³⁴Ba. In the de-excitation process, 11 γ-emissions are identified [11]. The coincidence window was set on 796 keV full-energy peak. The liquid scintillation samples were prepared by filling 20 mL standard glass vials with 10 mL of unquenched Ultima Gold liquid scintillator (PerkinElmer, Waltham, MA, USA). The observed counting rates were from 3×10³ s⁻¹ to 6×10³ s⁻¹. The measurement was carried out for 14 counting intervals for each prepared sample by displacing three PM tubes up to 45 mm from a counting sample, up to 30 mm in steps of 3 mm and then to 45 mm in steps of 5 mm. Backgrounds were measured likewise.

Fig. 3 shows logical sums of three double coincidences rate (N_D) observed at each counting interval with a sample. As the β-detection unit, three PM tubes, was moving away from a centrally located counting vial, it was decreasing absolutely up to 30% according to our data, thus expecting to obtain the efficiency function defined on a sufficient region to extrapolate linearly. Inset shows observed background versus displacement. It was about 3.3 s⁻¹ to 1.2 s⁻¹ for every cases of measurement. For the case of a sample of count rate of 3,000 s⁻¹, effects of background on observed activity is about 0.08% according to data. It was 0.57% with our earlier method (Table 1), so it was a major factor in reducing measurement accuracy. However, we could confirm the backgrounds due to thermal noises or after-pulses were almost rejected at coincidence channel to negligible levels.

The dead time of each β- and γ-counting channel was adjusted to be non-extending type of 20 μs (see next paragraph). The true coincidence rate ρ_βγ, true β count rate ρ_β (=N_D), true γ count rate ρ_γ and β-detection efficiency ɛ_β (=ρ_βγ/ρ_γ) were corrected and determined by using the mathematical formula derived by Cox and Isham [12], and completed by Smith [13].

Fig. 4 shows a plot of an efficiency function obtained at each counting interval. The parameter of x-axis is (1−ɛ_β)/ɛ_β and y-axis is N_D/(ɛ_β×m) where m is the mass of a considering sample. The observed values of β-detection efficiency ɛ_β were 0.54≤ɛ_β≤0.81. The N_D/(ɛ_β×m) were varying linearly on the whole counting interval, thus could be linearly extrapolated to (1−ɛ_β)/ɛ_β=0, so ɛ_β=1, by the least-squares method for a plot of N_D/(ɛ_β×m) versus (1−ɛ_β)/ɛ_β. The average of the weighted mean value is 396.3±1.7 kBq/g (Table 1), at reference date. The uncertainty was calculated from the square root of the summed squares of each uncertainty component as shown in Table 1. The largest uncertainty component was due to the curve fitting. The KRISS certified value is 396.0±2.0 kBq/g. It is consistent with ours within uncertainty limit.

Concerning the duration of dead-time, it usually applies long length of extending type, for example 30 μs or more, to reject the after-pulses with conventional TDCR method [3–5]. Since we have applied non-extending type for all β- and γ-counting channels, it was necessary to determine the appropriate width of dead-time and also to investigate the effects of after-pulses or other factors on measured values. For this, activity-deviations due to the duration of dead time were observed with non-extendable width varying from 5 μs to 40 μs. All measurement cases were performed as described above. To see it more clearly, it has been done with a sample with relatively high counting rate of 6×10³ s⁻¹.

The results obtained from each selected width (Fig. 5), were uniformly distributed around the value at 20 μs. The biggest difference was observed between the data of 5 μs and of 15 μs and it was 0.26% at most. In fact, any notable effects due to after-pulses or other factors on activity determinations could not be found according to our data. So, it was adjusted to be 20 μs of non-extending type with a standard uncertainty of 0.05% for our system.