Overview
The transfer function T depends not only on energy but also on numerous other parameters. These dependencies must be determined in an extended description of the transfer function before the procedure for the experimental determination of individual parameters can be described.
In the first step, the transfer function is treated in an evaluation model for measurements in open geometry. This measurement method can be regarded as a special case of a segmented measurement with only one measurement position. The generalization for the evaluation of segmented gamma scan measurements in other measurement modes (spiral scan, multiple disk scan) is described in the section collimated geometry.
Evaluation Model for Measurement in Open Geometry
The evaluation model is based on the description by Filß for measurements in open geometry. It was developed in 1995 and allows for the calculation of the corresponding activities for waste containers (cylindrical containers) with homogeneous distributions of matrix and gamma-emitting nuclides of the waste product. Originally developed for the characterization of 200 L waste containers, it also finds application in the activity determination in cylindrical containers of other dimensions, such as MOSAIK containers or 30 L plastic barrels with waste products. The method can also be used for the activity determination of other activity-bearing contents, such as for cylindrical volume sources for calibration purposes. In a specific question, the method was successfully used for activity determination on cubic 1 m3 containers.
The relationship between the measured count rate Z and the activity A is described in this evaluation model by the following equation.
\[ A = M \cdot \left[ \frac{1}{\epsilon} \cdot \frac{1}{\eta} \cdot \left( \frac{\mu }{\rho} \right) \cdot \frac{1}{F_0} \cdot \frac{K_2}{K_1}\right] \cdot Z\]
| A | Activity in Bq |
| M | Mass of the container content (net mass) in g |
| η | Emission probability of the examined gamma line |
| ε | Effectiveness of the detector for a point source on the container surface |
| (μ/ρ) | Mass attenuation coefficient of the matrix for gamma radiation in g·cm-2 |
| F0 | Cross-sectional area of the container projected onto a sphere around the detector (radius = distance from detector to container) in cm2 |
| K1 | Correction factor for the attenuation in the matrix, resulting from averaging the field of view of the container surface in the detector |
\[ K_1 = \frac{1}{F_0 } \int _{F_0} \left\lbrace 1-\exp(-\mu \cdot B) \right\rbrace dF\]
| F0 | Area of the container cross-section in cm2 that is “seen” by the detector |
| μ |
linear attenuation coefficient for gamma radiation in cm-1 |
| B | Path length of the beam in the matrix in cm |
| K2 | Correction factor for the attenuation in the container wall |
\[ K_2 = \exp(\mu_w \cdot w^{*}) \]
| μw | linear attenuation coefficient of the container wall (typically iron) for gamma radiation in cm-1 |
| w* | w* = 1.25 · w with w wall thickness of the container in cm |
| Z | Count rate in s-1 |
The parameters, their respective physical meanings, and ranges of values are also described in detail in the section “Physical Meaning of Individual Parameters of the Transfer Function According to Filß for Open Geometry”.
The transfer function T corresponds in the above equation to the expression in square brackets.
\[ T = \left[ \frac{1}{\epsilon} \cdot \frac{1}{\eta} \cdot \left( \frac{\mu }{\rho} \right) \cdot \frac{1}{F_0} \cdot \frac{K_2}{K_1}\right] \]
A derivation of the equation can be found in Derivation of the Transfer Function According to Filß.
Assumptions
The validity of the evaluation procedure is based on the following assumptions:
- The waste container is a cylindrical container.
- The contents are homogeneous, i.e., the following holds:
- 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.
- The attenuation of the gamma rays when passing through the container wall with thickness w is described by a mean shielding factor K2 that typically assumes values close to 1.
- The detector is calibrated with a point source that is located on the surface of the container or at a distance S directly opposite the detector. The energy-dependent effectiveness ε is calculated from the count rate Z0 and the activity A0 of a radionuclide in the point source, whose examined characteristic gamma line has the emission probability η0 according to
The assumptions suggest that the only experimentally determined parameter is the energy-dependent effectiveness ε of the detector for the detection of incoming gamma radiation. All other parameters must be known a priori according to the assumptions and can partly be obtained from corresponding databases.
