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The model of gamma ray registration with detectors of different size Polimaster® © 2013

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The model of gamma ray registration Let us consider the registration of gamma rays on the example of raindrop collection from the surfaces of different sizes - large, medium, small, as an analogue of size and operation of Geiger-Mueller counters registering flying gamma quanta. For clarity and uniformity of calculations for different sizes of surfaces, we assume that the water drops (gamma quanta) on each surface (detector) will occur with the same frequency (periodicity) - 1 out of 6 (you can take a different ratio). The randomness of the distribution of dripping we will obtain by displacing the distribution of drops on the surface area. The step of dripping we will take as over one cell (step). Then we will compare the results of drop collection from every surface and in the end determine the dependence of the number of drop caught on the size of the surface. We will hold four iterations of collecting drops (registration) using this distribution of drops on the surface and shifting cells each time by one. 123456789101112131415161718192021 2 3 Polimaster® © 2013 periodicity step

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6x3=18 cells 3x3=9 cells 1x3=3 cells 123456789101112131415161718192021 2 3 We cut out a fragment of the table and divide it into multiple segments of different sizes Polimaster® © 2013 The sizes of detectors (Geiger-Mueller counters): Big Medium Small The model of gamma ray registration

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rain drops Polimaster® © 2013 The model of gamma ray registration

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3 drops 18 cells 3 drops 18 cells 3 drops 18 cells 3 drops 18 cells 2 drops 9 cells 1 drop 9 cells 2 drops 9 cells 1 drop 9 cells 0 drops 3 cells 1 drop 3 cells 0 drops 3 cells 1 drop 3 cells The scheme clearly shows that a large area of collection is more even, and in smaller areas individual results may have variation of 50% and more of final average value. Polimaster® © 2013 The model of gamma ray registration

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Polimaster® © 2013 We sum how many drops were collectes in four iterations on different surfaces The model of gamma ray registration

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12 drops/ 18 cells 6 drops/ 9 cells 2 drops/ 3 cells Overview of the results of the accumulation ondifferent sizes : Sizes 6x3= 18 cells 3x3=9 cells 1x3= 3 cells Big Medium Small 2/3 In each case the collected number of drops is proportional to the size and the proportion is the same! = = Polimaster® © 2013 The model of gamma ray registration

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According to described model we can conclude: When using detectors of different sizes the number of pulses registered varies in proportion to the size of the detector. Using the algorithm of converting a number of pulses by the size of the detector we can obtain unified results for detectors of different sizes. Smaller detectors require more iterations of pulse detection to obtain correct average data, so it is necessary to carry out more measurements. Polimaster® © 2013 The model of gamma ray registration

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On this basis we can estimate the advantages and disadvantages of different size of detectors: Polimaster® © 2013 The model of gamma ray registration BigMedium / small ADVANTAGES Quick collection of statistics, small time for averaging the results of measurements with the required accuracy Small size and weight of the instrument, a better performance of battery set Small price of the detector and the device Large size and weight of the device Small operating time of battery set High price of detector and device Time needed to collect statistics for averaging the results of measurements with the required accuracy SHORTCOMINGS THE RESULTS ARE SAME! when working properly with the devices

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