Measurement on an identical measurement object with known activity A
A very simple, yet rarely applicable method for determining the activity A from the count rate Z measured in open geometry is based on a comparison measurement. This is conducted with an object that matches the dimensions, content (material distribution, radionuclides), and activity distribution of the object to be measured, whose activities Aref are known.
In a measurement of the comparison object, the count rates Zref of the various characteristic lines of the radionuclides are determined. Subsequently, the comparison measurement is carried out in the same measurement geometry with the object to be characterized, and the corresponding count rates Z are determined. By applying the rule of three, a simple relation arises
\[ A = \frac{a_{ref}}{Z_{ref}} \cdot Z \]
which allows the unknown activity A to be determined without the need for explicit calculation of a detector efficiency.
This method can particularly be applied in measurements of continuous waste streams, where it is ensured that the content and nuclide vector do not change over time.
Measurement with calibration source and inclusion of model descriptions of the measurement arrangement
The assignment of a count rate Z to an activity A for a measurement geometry is generally done through a mathematical model of the form
\[ A = T \cdot Z \]
The parameters contained in the energy-dependent transfer function T, which are independent of the measurement object, are summarized into energy-dependent efficiency calibration factors. Their description depends on the chosen evaluation procedure.
Evaluation procedure according to Filß
In the evaluation model according to Filß for measurements in open geometry, the energy-dependent efficiency ε of the detector enters as the only parameter independent of the measurement object. A prerequisite is that the calibration measurement is performed with a point source located at the same distance S from the detector as the surface of the later measurement object.
Then the energy-dependent detector efficiency values ε can be determined by one (or more) measurements with suitable calibration sources (activities A0, emission probability η0 of the respective characteristic gamma line) from the measured count rates Z0 (Note: the equation applies to each energy):
\[ \epsilon = \frac{Z_0}{A_0 \cdot \eta_0} \]
The calibration sources are to be selected such that their characteristic lines cover the entire energy range that will be analyzed in later measurements with a sufficient number of values.
If the distance Skal of the calibration source from the detector deviates from the distance S in the later measurement of the measurement object (for example, if the diameter of the examined container varies), the effectiveness value must be corrected accordingly by applying the inverse square law:
\[ \epsilon = \frac{S_{kal}^2}{S^2} \cdot \epsilon_{kal} \]
For the efficiency calibration, it is assumed that the efficiency ε has no angular dependence. This is approximately given with the recommended distances for the measurements.
