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\section{Introduction}  \subsection{Muon Decay}  The muon,$\mu^{-}$, is an elementary particle and is classified as a negative lepton. In keeping with all other elementary particles, the muon has a corresponding antiparticle of opposite charge, $\mu^{+}$, known as an antimuon. The muon is an unstable particle, with a mean lifetime on the order of a few microseconds. Muons decay by the weak interaction into an electron , an electron antineutrino, and a muon neutrino. In a similar fashion antimuons decay into a positron, an electron antineutrino, and a muon neutrino. In formulaic terms, these decays are represented below.   \begin{equation}  \mu^{-}\rightarrow e^{-}+\bar{\nu}_{e}+\nu_{\mu} 
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\begin{equation}  \mu^{+}\rightarrow e^{+}+\nu_{e}+\bar{\nu}_{\mu}  \end{equation}  Muons are formed high in the earth's atmosphere by energetic cosmic rays, which produce a shower of particles, some of which are charged pions that will eventually decay into muons. The muons then rain down through the atmosphere, eventually decaying themselves. Due to relativistic time dilation, they appear to live longer to observers in the Earth's reference frame than in their own. Otherwise, they would be significantly less likely to reach sea level. As the muons travel toward the earth, a scintillation detector is all that is needed for detection. The details concerning the structure of the scintillator and detection of muon decays will be explained in our procedures. The purpose of this particular experiment is to study the decay of muons at 190 ft above sea level. We do so by measuring the mean muon lifetime, $\tau$, the ratio of positively charged muons to negatively charged muons $\rho$, muon flux $\phi$, and the Fermi Coupling Constant $G_{f}$. Details on the computation involved in determing these characteristics will be deferred until our analysis. It is important to note that the muon and the antimuon should have the same mean lifetime in a vacuum, but will have a different mean observed lifetime in this experiment. Thus is due to the fact that negative muons can interact with protons through the electroweak force, thus shortening their lifespan. \subsection{Gamma-ray Spectroscopy}  In addition to Muon decay an experiment was conducted to examine gamma rays and their interactions with matter. In order to detect the gamma rays, the gamma ray enters a NaI:Tl scintillator crystal where it produces a rapidly moving electron. As the electron moves through the crystal, it loses its energy through excitation of the ions in its path. This excitation energy is given off by emission of visible light. The photons that are given off from excitation energy are detected by the photosensitive surface of a photomultiplier tube. The photons then eject electrons via the photoelectric effect. These electrons produce a current pulse, which is converted to a voltage pulse. In this way the height of the voltage pulse is proportional to the number of electrons, which is proportional to the number of photons, which is in turn proportional to the initial energy. When a radioactive source is placed near the scintillator the photomultiplier will produce a series of voltage pulses, which correspond to the decay of a single nucleus in the source. A multi-channel analyzer then sorts the voltage pulses according to their height and counts them in order to give a spectral energy distribution of the electrons. \textbf{Figure} shows an example of the spectral energy distribution.