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3D calculations for counting

Dear Reader,

Here we go, we will start with a C60 molecule as this gives us a close to perfect sphere. I then read the cif file into ORTEP and then generated a xyz table of atomic positions. This table was then opened in EXCEL and it was found that the average location of all the carbons was at 0, 0, 0 which is perfect for the uniform sphere.

The average radius of this sphere is 3.535 Å and the ESD is 0.008 Å so I think that we are dealing with a nice sphere so lets get to work.

After scaling up the C60 sphere to make it one with a radius of 14.5 cm I used the inverse square law to estimate the amount of radiation which would reach the points on the sphere in total when the source was at the centre of the sphere. I repeated this calculation with the source being displaced along the x axis. Due to the fact that I was only using 60 points on the surface of the sphere I choose to simulate a 4π geometry with a series of 60 point detectors which are 50 cm from the centre of the sphere.

I did a quick calculation and I found that this gave only a very small deviation from the expected constant sensitivity which I was expecting for the 4π geometry when attenuation in matter was ignored. The deviation was smaller as I increased the distance between the detectors and the source so I increased the distance between the detectors and the centre of the sphere to 10 meters.

Using the linear attenuation coefficient for water and Cs-137 I then worked out the attenuation for photons for each point and each distance through the water sphere. I was a little shocked, the results of the calculation suggested that the location of the point source in the water sphere had almost no effect on the counting efficiency. Also the centre of the sphere was slightly more sensitive (9 %) than parts near the surface. This was a slight shock. I think it is due to the fact that a photon will on average have to pass through more of the sphere to reach the surface when the source is moved away from the centre.

When the linear attenuation coefficient was increased to simulate low energy photon emitters like iodine-131 the point source near the surface was more sensitive. I will do some more calculations and then I will show you the graphical results soon.


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