Measurement of the geometric efficiency

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Determining the geometric efficiency is essential for calculating the total activity of a sample. This is to be demonstrated here as an example, for other experimental setups, the procedure can be adapted accordingly.
In the present case, is used a cylindrical sample located beneath a cylindrical detector within a lead shield. This is a quite typical setup.
Geometric efficiency depends on the solid angle between the sample and the detector. Consequently, it is smaller at the sample's surface bigger than at its bottom. Therefore, the sample is virtually divided into thin slices, and the calculation is performed for these.
Different formulas or Monte Carlo calculations are is often used for this,However, more accurate results are achieved through experiments. For this purpose, a very thin disc of radioactive material is measured at varying distances from the detector.
The container consists of a flat dish into which a heavy mineral concentrate was filled. The sample was mixed with a solution of colophon (rosin) in ethanol; after drying, it is fixed, but the colophon can be completely redissolved without leaving residues.
Since the specific activity of the sample was not very high and the sample mass was low (7g), very long measurement times (32 hours each) were necessary. Measurements were carried out at 6 distances from the detector.
Measurements were taken at anode voltages of 610 V and 640 V. A third-degree polynomial was calculated.

Result for 640 V

f(x) = − 0.000007113 x3 + 0.000923081 x2 − 0.045013525 x + 1.000000000
R2 = 0.999645086

Result for 610 V

f(x) = − 0.000006861 x3 + 0.000899674 x2 − 0.044301053 x + 1.000000000
R2 = 0.999761614

Correction Factor

f(x) = − 0.000014515 x3 + 0.001800713 x2 + 0.039621323 x + 1.000000000
R2 = 0.999319947

The results are practically identical, with the coefficient of determination exceeding 99.9%. "Factor" refers to the factor by which the values for the individual slices must be multiplied when determining the self- absorption.
However, the results relate only to the geometric efficiency between the slice and the detector. To determine the total activity, the opposite direction must also be considered. Therefore, the determined values for the geometric efficiency must be divided by 2, and the factor must be multiplied by 2.

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Drawings, diagrams and additional Information you will find on SourceForge.net -> doc -> HowTo -> English -> Determining_the_geometric_efficiency.pdf