I played around a little bit after you guys left. I think I know how a 2 degree shift happens and how to fix it.
Turns out it is probably due to the position of the source. We'll try to make a holder for the source to get rid of the problem.
First, lets try to calculate what is likely to happen to the sweet spot, or the position where the maximum occurs if we move the source away from center.
Now, to measure this, I found the sweet spot by watching the rate at which counts arrived and moving the source around. I taped a meter stick to the table so I could look at the relative position away from the spot I chose
In the plots below, I first did a scan of the source to see how close I came to the sweet spot. Think I got it within 1/2 mm. Then I moved the source and looked at the change in the sweet angle for a change in the source position.
In the plot below, I show the results of the test. Pretty much what we expected. The solution I think is to make a new source holder.
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