\section{Results and discussions}
\subsection{Titanium}
Fitting the peak around \SI{932}{keV} in the photon spectrum gives energies of the $2p_{3/2}-1s$ and $2p_{1/2}-1s$ transitions as \SI{932.5 \pm 0.9}{\keV} and \SI{930.4 \pm 1.1}{\keV}, respectively. These values are consistent with previously reported values by Wohlfahrt et al.~\cite{Wohlfahrt1981} given the isotopic abundance of the natural titanium target used in this experiment. The 
number of $(2p_{3/2}-1s)$ X-rays is:
\begin{equation}
  N_{2p_{3/2}-1s} = (11881 \pm 591) \,.
\end{equation}

\begin{figure}[tbp]
  \centering
  \includegraphics[width=0.8\textwidth]{figs/ti_931keV_fit}
  \caption{Fitting $(2p-1s)$ peaks on \ce{^{nat}Ti}}
  \label{fig:ti_931keV_fit}
\end{figure}


Emission rates of K X-rays from titanium is listed in~\cref{tab:kXraysTi}.

\begin{table}[tbp]
  \centering
  \caption{Emission rates of K X-rays from titanium}
  \label{tab:kXraysTi}
  \begin{tabular}{ccc}
    Transition & Energy [keV] & Rate [\%] \\
    $2p-1s$ & 932.4 & \num{78.9\pm2.5}\\
    $3p-1s$ & 1121.5 & \num{7.5\pm1.7}\\
    $4p-1s$ & 1187.9 & \num{3.2\pm1.0}\\
    $5p-1s$ & 1218.5 & \num{2.6\pm1.4}\\
    $6p-1s$ & 1235.2 & \num{3.2\pm1.9}\\
  \end{tabular}
\end{table}

\begin{figure}[tbp]
  \centering
  \includegraphics[width=0.8\textwidth]{figs/ti-kXrays.pdf}
  \caption{Muonic X-rays in the Lyman series from titanium}
  \label{fig:ti_kXrays}
\end{figure}

\subsection{Aluminum}
\label{subsec:result_al}

\begin{figure}[tbp]
  \centering
  \includegraphics[width=0.8\textwidth]{figs/al-kXrays.pdf}
  \caption{Muonic X-rays in the Lyman series from aluminum}
  \label{fig:al_kXrays}
\end{figure}

Emission rates of K X-rays from aluminum is listed in~\cref{tab:kXraysAl}.

\begin{table}[tbp]
  \centering
  \caption{Emission rates of K X-rays from aluminum}
  \label{tab:kXraysAl}
  \begin{tabular}{cccc}
    Transition & Energy [keV] & Intensity (this experiment) [\%] & Intensity [\%]~\cite{Measday2007}\\
    $2p-1s$ & 346.8 & \num{83.1\pm3.5} & \num{79.8\pm0.8}\\
    $3p-1s$ & 412.8 & \num{7.71\pm0.29}& \num{7.6\pm1.5}\\
    $4p-1s$ & 435.9 & \num{4.79\pm0.18}& \num{4.9\pm1.0}\\
    $5p-1s$ & 446.6 & \num{3.81\pm0.14}& \num{3.9\pm1.0}\\
    $6p-1s$ & 452.4 & \num{2.24\pm0.13}& \num{2.2\pm1.0}\\
  \end{tabular}
\end{table}
