Effect on Muon Rate of Using Various Absorbers
Your goal is to see what effect placing various materials in the path of the muons has on the rate at which muons pass through the apparatus.†† As muons pass through a substance, they lose energy, so you expect absorber materials to decrease the muon rate, but we want to know how much and how it depends on characteristics of the absorbing material.†† It would be best to use the same thickness of all the different materials.† However, if you canít make them all the same thickness, you must calculate the rate per unit thickness of absorber.
You should place the detectors one above the other with the various absorbing materials placed either above or between them.† You must keep the location of the absorbing material relative to the paddles constant throughout the experiment. Of course you will need pieces of absorber material with a large enough surface area to insure that muons cannot travel thru the scintillators and miss the absorber material!!† Also, of course, you will need to intersperse your experimental runs with control runs, that is, with no absorber at all. So, you will need to record information on the type and thickness of the absorber material, the time and coincidences for your runes, as well as some general information about how you set up the paddles and absorber.†
First, you need to calculate the muon rates for your various runs. Then calculate the uncertainty in those rates, it equals the square root of the counts, divided by the time.† Next, find the difference caused by each absorber by subtracting the rate with no absorber from the rate with an absorber. The uncertainty in this difference is found by squaring the uncertainties of the rates both with and without absorbers, taking the sum of those two squares, then taking the square root of that sum!† See the equations below: