William P. Gammel edited par_The_entire_set_up__.tex  over 8 years ago

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\par The entire set-up of our experiment consisted of a plastic scintillator, a photomultiplier tube, a signal amplifier, a discriminator, and a FGPA timer. Muons which enter the scintillator transmit some energy to molecules that are present, thus exciting electrons in the molecule to higher energy states. The excited electrons then emit light before returning to their initial energy level. Then when a muon decays inside the scintillator, the newly formed electron will emit light as well. The time between the two light pulses is the measure of the muons lifetime. As was mentioned earlier, not all light pulses represent decay, thus some measures must be taken to filter out these unwanted events. There are three main methods by which we can correct for these unwanted occurrences. The machine itself partially compensates for the issues by resetting its internal timer if it does not detect a successive signal after a initial pulse within $12 \mu\textrm{seconds}$. It is assumed that if the successive pulse is greater than $12\mu\textrm{seconds}$ then the muon did not decay within the scintillator. For example, a muon can decay twice in $12 \mu$ seconds if each decay is $6 \mu$ seconds. The bin setting was chosen to give the most detail in the spectrum. The bin size was chosen to be 60, which meant that there were 60 different bins the muon decays could fall into. Smaller bins would have resulted in a less detailed spectrum. It should also be noted that the threshold potential of the discriminator was varied in order to determine the threshold voltage that would allow the event to be counted. The threshold voltage was set at $88\textrm{mV}$ such that the muon counter gave a flux of $1 muon min^{-1}cm^{-2}$, which is what is predicted for muon flux around sea level. A summary of the parameters can be found in Table (). A computer software program called \textbf{Muon} also helps to compensate, by employing an algorithm called \textbf{Sift} to remove unwanted data from the raw data times. After data was run through \textbf{Sift}, it was loaded into Igor Pro where it was graphed and fit to an exponential function. The mean muon lifetime as determined from our fit was $2.04\pm0.04 \mu\textbf{seconds}$, which was within the range of the accepted value, $2 \mu \textrm{seconds}$ . Furthermore we expect our mean muon lifetime to be slightly different from the accepted value since negative muons can interact with protons through the electroweak force, thus shortening their lifespan.  \par Relativistic time dilation could not be confirmed for our experiment, since we only chose to take take data at a single elevation, 190 ft above sea level. Nonetheless we were able to calculate a myriad of important muon characteristics from our data.   As discussed above in the Introduction, our apparatus was set up to measure cosmic rays going through the scintillator. But, the computer would only record a true muon if it decayed within the scintillator. We gave this a time limit of $12 \mu$ seconds, as seen in Table \ref{table:muonsettings}. The time given just means that we chose an amount of time that the muons had to decay within. For example, a muon can decay twice in $12 \mu$ seconds if each decay is $6 \mu$ seconds. The bin setting was chosen to give the most detail in the spectrum. 60 bins meant that there were 60 different bins the muon decays could fall into. Smaller bins would have resulted in a less detailed spectrum.