NUMERICAL EXAMPLE : ¹⁴C

We measured 5 vials containing 15 mL of toluene-based liquid scintillator and a ¹⁴C radioactive solution. The measured counting rates, in counts per minute (cpm), and the quench parameters of the samples are listed in Table 1. The quench parameter, q, can be anyone of the well known external standard quantities : Horrocks H^#, SQP(E) or tSIE.

Table 1. Experimental counting rate and quench factor for C-14.

Our goal is to obtain the counting efficiency and the activity of each one of these 5 samples by applying the CIEMAT/NIST method.

We prepared and measured 6 vials containing the same volume of the same scintillator used to prepare the ¹⁴C samples and known amounts of a tritium standard solution. These sources were then gradually quenched by adding nitromethane to create a quenched set of tritium sources. The obtained calibration curve is given in table 2.

Table 2. Calibration curve of tritium

Applying a computation model we have obtained the counting efficiency as a function of the free parameter for tritium. The results are shown in Table 3.

Table 3. Computed counting efficiency for selected values of the free parameter

Now, we take each one of the counting efficiency values for tritium from Table 2, and by interpolating into Table 3, we compute the corresponding free parameter. We apply here linear interpolation to facilitate the work. However, the best way of working is fitting a curve to the data in Table 3 or compute the counting efficiency for very close values of the figure of merit. Variations of l of 0.005 allows one to determine the chemical quench parameter for each value of the figure of merit without interpolations. The obtained results are presented in Table 4.

Table 4. Universal curve for 15 mL of toluene based liquid scintillator

The same model used to compute Table 3 can be applied to compute the counting efficiencies for different values of the free parameter for ¹⁴C. The results are shown in Table 5.

Table 5. Counting efficiencies of ¹⁴C for different free parameter values

We need to obtain the corresponding counting efficiency for each value of the free parameter in Table 4. This is carried out by interpolating each parameter value in Table 5. The calibration curve obtained by this procedure is given in Table 6.

Table 6. Computed calibration curve of ¹⁴C

Now we can compute the counting efficiency and the activity of the samples in Table 1. By interpolating in Table 6 each chemical quench value in Table1, we obtain the corresponding counting efficiency shown in column 3 of Table 7. The activity, in KBq, can be computed from the counting rate (column 2) and the counting efficiency. The results are presented in column 4 of Table 7.

Table 7. Counting rate, counting efficiency and activity of ¹⁴C

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