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William P. Gammel edited section_Discussion__.tex
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\section{Discussion}
\subsection{Muon Decay}
Several key characteristics of muons were identified in this experiment. The most important feature was perhaps the mean muon lifetime, $\tau_{obs}$, for this variable was critical in the calculation of positive to negative muons and the Fermi Coupling Constant. Statistically, the fit of our data to the exponential function expressed in Equation 3 is good, since our function has a $\tilde\chi^{2}$ value of 0.6211. Thus our data matches the expected behavior of muon decay distribution. Furthermore our result, $\tau_{obs}=2.04\pm0.04$ agrees with the accepted value of muon lifetime within uncertainty. Thought the observed result $\tau_{obs}=2.04\pm0.04$ fails to agree with the accepted value of antimuon lifetime, it is assumed this incongruity is an indicator that many more muon decays were observed than antimuon decays, and thus the average lifetime was weighted. This is quite interesting, since we had previously hypothesized that since positive muons do not have the potential to interact with matter we would see more of them than negative muons, which can vanish prior to decay due to interaction with material inside the scintillator. Nontheless, our computation of the ratio between positive and negative muons, $\rho=0.072$, was quite small, which confirmed our conclusion that there were many more negative muon decays observed than antimuon decays.
\par Finally, our calculated value for the Fermi Coupling constant, $G_{F}$, was close to the accepted value, but failed to match the value within uncertainty. However, the discrepancy is not particularly problematic, since $\tau_{obs}$ was an average of the mean muon lifetime and the mean antimuon lifetime. Therefore $\tau_{obs}$ is not expected to match the mean muon lifetime in a vacuum. Since the Fermi Coupling constant is calculated using the mean muon lifetime in a vacuum, it would make sense that the value observed and the accepted value did not match within uncertainty.
\subsection{Gamma Ray Spectroscopy}
