Collimated Geometry - Evaluation Model According to Filß
Overview
The transfer function T depends not only on energy but also on other parameters. These dependencies must be determined in an extended description of the transfer function before the procedure for the experimental determination of the individual parameters can be described.
In this section, we consider the transfer function T in an evaluation model for segmented gamma scan measurements in collimated geometry. The evaluation model can be applied to a variety of measurement modes (Spiral scan, Multi-disk scan).
Evaluation model for measurement in collimated geometry
The evaluation model is based on the description by Filß for measurements in collimated geometry. It was developed in 1989 and allows for the calculation of the associated activities for waste containers (cylindrical containers) with homogeneous distributions of matrix and gamma-emitting radionuclides in the waste product. The actual waste matrix can also be located in a cylindrical inner container that is symmetrically placed inside the waste container and surrounded by a homogeneous matrix (often cement).
The relationship between the measured count rate Z and the activity A is described in this evaluation model by the following equation:
\[ A = M \cdot a = M \cdot H^{‘} \cdot \left( \frac {\mu}{\rho} \right) \cdot \frac{K_2 \cdot K_3}{K_1} \cdot \frac{1}{\eta} \cdot Z \]
| A | Activity in Bq |
| M | Mass of the container content (net mass) in g |
| a | Specific activity in Bq/g |
| H' | Energy and geometry-dependent calibration factor in cm-2 |
| (μ/ρ) | Mass attenuation coefficient of the matrix for gamma radiation in g·cm-2 |
| K1 |
Correction factor for attenuation in the matrix, resulting from averaging the field of view of the container surface in the detector \[ K_1 = 1-\exp \left(-\mu \cdot h\right) \]
It holds: \(K_1 \approx 1\) for large containers (h large) and dense matrices. |
| K2 |
Correction factor for attenuation in the container wall and internal shielding \[ K_2 =\exp \left( \sum\limits_{i=0} -\mu_i \cdot d_i \right) \]
|
| K3 |
Correction factor for the fraction of measurement time to the total measurement time while the part of the container with the active matrix is in the detector's field of view. \[ K_3 = \frac{T}{T^{*}} \approx \left(\frac{h}{h^{*}} \right) \]
|
| η | Emission probability of the characteristic line |
| Z | Count rate in s-1 |
The parameters, their respective physical meanings, and ranges are also discussed in detail in the section "Physical significance of the individual parameters of the transfer function according to Filß for open and collimated geometry".
The transfer function T corresponds to the expression in square brackets in the above equation:
\[ T = \left[H^{'} \cdot \left( \frac{\mu }{\rho} \right) \cdot \frac{K_2 \cdot K_3}{K_1}\right] \]
A derivation of the equation can be found in Derivation of the transfer function according to Filß in collimated geometry.
Assumptions
The validity of the evaluation procedure is based on the following assumptions:
- The waste container is a cylindrical vessel.
- The content of the activity-bearing matrix is homogeneous, i.e. the following holds
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- The density: 𝜌 = constant (unit: g·cm-3)
- The specific activity: a = constant (unit: Bq·g-1)
- The activity concentration: CA = constant (unit: Bq·cm-3)
- The material of the waste product is known.
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- If the activity-bearing material is in a cylindrical inner container, then this is symmetrically aligned with the axis of rotation in the waste container.
- The attenuation of gamma rays when passing through the container wall and additional internal shields with thicknesses di and linear attenuation coefficients µi is described by an average shielding factor K2 that typically assumes values close to 1.
- The energy- and material-dependent calibration factor H is determined in calibration measurements with suitable point, area or volume sources.
