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William P. Gammel edited section_Results_subsection_Muon_Decay__.tex
over 8 years ago
Commit id: 17a8740523c2df513b1d41dca1ed2206b1ee9a47
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\end{equation}
Where $\tau^{+}$ is the known value of the mean lifetime for an antimuon,$2.19 \mu second$, $\tau^{-}$ is the known value of the mean lifetime for a muon, $2.03 \mu seconds$, and $\tau_{obs}$ is the value $2.04\pm0.04 \mu seconds$, taken from the best fit of our data.
Thus the calculated ratio is approximately $0.072\pm.001$. This value is quite small, which confirms our previous hypothesis that the number of muon decays detected was significantly greater than the number of antimuon decays detected.
\subsubsection{Muon Flux} \subsubsection{Fermi Coupling Constant}
The Fermi Coupling Constant is the strength of the weak force, and can be calculated from the observed muon lifetime, $\tau_{obs}$. The relationship between the muon lifetime and the Fermi Coupling Constant is shown below,
\begin{equation}
\tau=\frac{192\pi^{3}\hslash^{7}}{G_{f}^{2}m^{5}c^{4}}
\end{equation}
In order to find the Fermi Coupling Constant we can rework the equation such that,
\begin{equation}
G_{f}=\sqrt[]{\frac{192\pi^{3}\hslash^{7}}{\tau m^{5}c^{4}}}
\end{equation}
\subsection{Gamma Ray Spectroscopy}
\subsubsection{Dertermining the Unknown Sample}