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\section{Experiment}  \subsection{Muon Decay}   Muons that are traveling down towards the earth can be detected by a scintillation detector. The scintillation detector contains a material that fluoresces when struck by radiation. A photomultiplier can then be used to measure this fluoresce, thus indicating when a muon has entered the detector. It is important to note that the detector will not only fluoresce when a muon it detected. Muon decay into a positron or an electron will also cause the detector to fluoresce as will almost any other radiation. A voltage discriminator can be used to screen out low energy events, but this alone will not eliminate all the background radiation.   \par The entire set-up of our experiment consisted of a plastic scintillator, a photomultiplier tube, and a signal amplifier. 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 $12 \mu seconds$. \mu\textrm{seconds}$.  It is assumed that if the successive pulse is greater than $12\mu seconds$ $12\mu\textrm{seconds}$  then the muon did not decay within the scintillator. 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 $88 mV$ $88\textrm{mV}$  such that the muon counter gave a flux of $1 muon min^{-1}cm^{-2}$, \textrm{muon min^{-1}cm^{-2}}$,  which is what is predicted for muon flux around sea level. 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 $2.04\pm0.04 \mu seconds$, \mu\textbf{seconds}$,  which was within the range of the accepted value, $2 \mu seconds$ \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.   \subsection{Gamma-Ray Spectroscopy}   When a gamma ray interacts with the NaI:Ti crystal the ray can give all of its energy to an electron via the photoelectric effect. The photoelectric effect will then cause a voltage peak in the spectrum seen by the photomultiplier, known as the photopeak. Data from the photomultiplier was used to first determine an unknown sample, and then to determine the age difference between two samples of Cs-137. As explained in the Section 1.2 the voltage pulse that is produced by the photomultiplier is measured by Analog to Digital Conversion (multi-channel analyzer). For a 10 bit ADC, the result is an integer value between 0 and 1023. Zero is assigned to a pulse less than $\frac{1}{100}$ of a volt, and 1023 is assigned to a pulse that is larger than about 8 volts. Thus pulses between 0V and 8V are proportionally given an integer value between 0 and 1023. This measure is known as the channel number, which the computer records. The resulting spectrum that is displayed is the number of gamma rays observed at each integer value plotted as a function of the channel number. Unfortunately, there is little information that can be extracted from information about the channel number, and thus we must calibrate our program so that there is some correlation between channel number and energy. In order to begin the calibration processes, optimal values for Voltage, Course Gain, and Fine Gain, which can be found in Table \ref{table:Gamma_Settings}, were found. To find these values an auto-calibration function provided by the program was first used on our samples. This allowed us to determine a basis for these settings, which we then modified slightly. The settings were varied so that our data closely matched published spectral data for both Cs-137 and Co-60.