Shower study documentation
Objective: the purpose of this study is to examine the ratio of particle shower frequency to shower size
Procedure: First we had to plateau all of our detectors. This entails fine tuning them using a voltmeter and locating the range of voltages(plateau) at which the particle count remains constant, but you can read more on that in the paper dedicated to it.
Once our detectors were plateaued, we arranged them in a rectangle so they were not overlapping at all and measured the total area covered by the detectors to be four hundred and eighty square inches disregarding the empty space in between them. We couldnt have the panels completely in contact due to the pvc pipes protecting the photomultiplier tubes getting in the way.
We marked a center point equidistant from each of the detectors and started running our trials with the detectors as close together as possible. We ran hour long trials, moving the detectors apart from each other in increments of one foot in both length and width, running a few trials at each new distance. It is important to note that as the detectors get further and further apart from each other, the ratio of the area encompassed by them to the area covered by them increases. The significance of this is that we can sort out the smaller showers from the larger ones as the larger ones can be picked up from any detector array size, whereas the smaller showers will be filtered out if they are too small to trigger a four fold coincidence in the larger, more spread out array
As expected, we got much higher coincidence rates when the detectors were closer together, though this doesnt necessarily mean that smaller showers are more common, because we were unable to devise a way to filter out bigger showers. So, we can determine that many showers are only a few feet in diameter, but without a much larger detector array, we cannot determine an exact percentage for any given shower radius.
Possible sources of error: our gate width was set to one hundred nanoseconds or (10^-7) seconds. Given this setting, as well as the fact that on average, a properly plateaued detector recieves about ten counts per second, or one count per tenth-second, and there are 10^7 sets of one hundred nanoseconds in one second, so if a muon is detected, the next one has a 1 in 10^6 chance of being detected in the same hundred nanoseconds. Therefore, if the first detection marks the start of the gate, then the three sucessive ones each have a chance of 1 in 10^6 of hitting within the gate time, so combined, the chances of four (individual, non-shower )hits in 100 ns is one in 10^18 in the space of a tenth of a second or one in 10^17 in the space of one second. So the chances of having a false positive for a shower is astronomically small. As for false negatives, our uneven, concrete ceiling could block or slow particles so they do not arrive at the detectors in an even layer. Also, since some showers come in at an angle not exactly perpendicular to the surface of the earth, different parts of these slanted showers can arrive at different times causing the detectors to not register a shower occurring even though there has been one.