\section{Data and Measurement}
\subsection{Energies}
The data that we measured in this experiment was stored in form of a histogram. There is no need to show the raw data, it's not very useful.\\
We started with a raw measurement of the energies of the gamma photons, which came out of our experiment for both photomultipliers. We expected two peaks at $511keV$ and $1275keV$ for the photons.


\begin{figure}[H]
\begin{center}
\includegraphics[width=0.8\textwidth]{picture/FullSpectrum.png}
\caption{Full spectrum by both photomultiplier}
\end{center}
\end{figure}


We recognise the two peaks at bin number $\sim 800$ and $\sim 1900$.\\
As next we chose the window of measurement for both photomultiplier. This will then give us the gate for the measurement on the digital converter.


\begin{figure}[H]
\begin{center}
\begin{subfigure}{0.45\textwidth}
\includegraphics[width=0.8\textwidth]{picture/511keV.png}
\caption{$511keV$ peak by PM 1}
\end{subfigure}
\begin{subfigure}{0.45\textwidth}
\includegraphics[width=0.8\textwidth]{picture/1275keV.png}
\caption{$1275keV$ peak by PM 2}
\end{subfigure}
\caption{Measured energy windows by both photomultiplier}
\end{center}
\end{figure}
\newpage


\subsection{Lifetime measurement}
Next we measured the lifetime of the positronium in aluminium and polymer.


\begin{figure}[H]
\begin{center}
\includegraphics[width=0.8\textwidth]{picture/LifetimeData.png}
\caption{Lifetime in polymer}
\end{center}
\end{figure}


\begin{figure}[H]
\begin{center}
\includegraphics[width=0.8\textwidth]{picture/LifetimeAluminium.png}
\caption{Lifetime in aluminium}
\end{center}
\end{figure}


At this point we quickly realize an asymmetric peak on the right side, about $100$ bins after the main peak. After some tries we changed a constant fraction discriminator and started a new set of measurement.


\begin{figure}[H]
\begin{center}
\includegraphics[width=0.8\textwidth]{picture/LifeTimeData2.png}
\caption{Lifetime in polymer}
\end{center}
\end{figure}


\begin{figure}[H]
\begin{center}
\includegraphics[width=0.8\textwidth]{picture/LifetimeAluminium2.png}
\caption{Lifetime in aluminium}
\end{center}
\end{figure}


Which looks much cleaner. We used this last measurements for future evaluation.\\