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\subsubsection{Charge Density}  Since we know that both have positive and negative muons contribute to the mean muon lifetime, it is also important to have some sort of quantantative understanding of the ratio, $\rho$ of muons to antimuons is. We can calculate $\rho$ via Equation ()   \begin{equation}  \rho=-\frac{\tau^{+}}{\tau^{-}}(\frac{\tau^{-}-\tau_{obs}}{\tau^{+}-\tau_{obs}}=\frac{N^{+}}{N^{-}} \rho=-\frac{\tau^{+}}{\tau^{-}}(\frac{\tau^{-}-\tau_{obs}}{\tau^{+}-\tau_{obs}})=\frac{N^{+}}{N^{-}}  \end{equation}  Where $\tau^{+}$ is the known value of the mean lifetime for an antimuon, $\tau^{-}$ is the known value of the mean lifetime for a muon, and $\tau_{obs}$ is the value (), taken from the best fit of our data.  \subsection{Gamma Ray Spectroscopy}  \subsubsection{Dertermining the Unknown Sample}  In order to determine what element the unknown sample was, we kept all the same settings from the calibration trial, so we already had a calibrated x-axis in energy, and kept the calibrations the same  in order to find the peak values of the unknown sample. We placed the unknown sample into the scintillator at the fifth slot from the top and the sample was within an old film container. The sample ran for $3670$ seconds Live Time. The difference between Live Time and Real Time is that as the program is producing the spectrum, there is a slight lag as it processes the data. So, the Live Time is the actual time the data is being recorded. By keeping the calibrations from trials 1 and 2, we were able to run the sample and have the data in Energy versus intensity instead of bins versus intensity. Beause we know the energy of the peaks it made it simple to find the element of the unknown sample. From the Smith College Physics radiation safety protocols version 5.0, we know that the only radioactive materials the sample could be are Cesium-137, Cobalt 60, Sodium 22, and Strontium 90. This reduced the error in our unknown sample because that left us with only four possible elements. As you can see in Figure \ref{fig:Unknown_Sample}, there are two peaks. After fitting gaussians to each peak (using Igor Pro), the first peak is at $0.53655 \pm 7.11 \cdot 10^{-5} \textrm{ MeV}$ and the second is at $1.2791 \pm 0.000406 \textrm{ MeV}$.