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progress14/XrayAnalysis.tex

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+The X-ray analysis is used to determine the number of stopped muons in the
+AlCap target by counting the number of
+muonic X-rays produced. In addition to the X-rays, there are gamma rays
+that can be observed and are relevant to Mu2e/COMET as well as AlCap.
+
+The entrance beam scintillator
+counters can be used to count the muons
+as they enter the vacuum chamber, however
+collimation and accounting for
+those muons that pass through the thin target,
+the stopping efficiency in the target is significantly
+less than 100\%. 
+
+The factor of interest for normalisation is the rate
+of muon nuclear capture inside the target. The branching ratio of
+capture is known for the targets of interest \cite{MeasdayAl} and is
+proportional to the number of muon stops.
+
+With the active silicon target
+we have a reliable method of detecting a stop, namely, an energy
+deposited in the silicon corresponding to the incoming muon beam energy, and
+a time coincidence between signals from the beam counters and the silicon
+detector. This is not the case with
+the passive silicon and aluminium targets, for which we use instead the muonic
+X-rays for normalisation.
+
+When a muon is captured by an atom, it gives off
+characteristic X-rays as it falls to the 1s state that can be counted
+to determine the stopping rate.
+For aluminium and silicon, the energies and intensities of the X-rays
+from the $2p\to1s$ transitions 
+are well known and listed in Table~\ref{tab:xray_ref}.
+The stopping rate
+can then be inferred from the number of these X-rays measured,
+after accounting for
+geometric and photo-efficiencies. The rate from this method was cross-checked with that determined directly from stops in the active
+silicon target, and the numbers are within each other's uncertainties.
+
+A peak from the natural background ${}^{214}$Pb (351.9 keV) exists near
+the ${}^{27}$Al \atrn{2p}{1s} ($K_\alpha$) X-ray.
+To suppress this neighbouring peak and the
+background, we required an entering muon in time coincidence with the
+germanium pulse. However, we noticed that an unexpected
+$\gamma$ line prompt with muon nuclear capture on lead appears at a slightly
+lower energy than the ${}^{214}$Pb line (Figure \ref{fig:xrayanalysis:tl207}).
+This is consistent with an intermediate excited
+state of $^{207}$Tl, produced by muon capture on $^{208}$Pb.
+Though not spoiling our measurement, the classification of
+this peak is important so that it can be confirmed in the next run.
+
+\begin{figure}
+  \centering
+  \includegraphics[width=0.5\linewidth]{figs/tl207.png}
+  \caption{To reduce the nearby pollution of the Al$_{K\alpha}$ by natural $^{214}$Pb,
+    only germanium signals within 300 ns of an entering muon were examined. When
+    the background peak persisted, we realised it was a prompt $\gamma$ from
+    muon capture on lead going via an intermediate excited $^{207}$Tl$^*$ state. This was
+    confirmed by the time structure of photons in that peak, which matches
+    the muonic lead lifetime.}
+  \label{fig:xrayanalysis:tl207}
+\end{figure}
+
+Though muonic X-rays are the primary method of normalisation in AlCap,
+there are others that can be used and since both Mu2e and COMET are interested
+in alternative normalisation schemes, it is important to examine the
+viability of other peaks as
+indicators of stopped muons. One is the $\gamma$ from the reaction
+$^{27}_{13}\mbox{Al}+\mu^-\to\nu_{\mu}+n+\gamma+^{26}_{12}\mbox{Mg}$, with an intensity of
+about 50\% per stopped
+muon and an energy of 1809 keV \cite{MeasdayAl}.
+What is appealing about this peak
+is that there are few nearby peaks to worry about, and the signal-to-noise
+ratio is
+favourable, see the data in Figure \ref{fig:xrayanalysis:mg26_1809}.
+The ratio of the number of observed
+counts in the 1809 keV gamma ray line relative to
+the $2p\to 1s$ muonic X-ray line is in good agreement with the value in the
+literature.
+
+\begin{figure}
+  \centering
+  \includegraphics[width=0.6\textwidth]{figs/mg26_1809keV}
+  \caption{The $\gamma$ produced in
+           $\mu^-+^{27}_{13}\mbox{Al}\to\nu_{\mu}+n+^{26}_{12}\mbox{Mg}^*$
+           followed by $^{26}_{12}\mbox{Mg}^*\to ^{26}_{12}\mbox{Mg}+\gamma$,
+           occurs at 1809 keV with an intensity of 0.51 per $\mu$-capture \cite{MeasdayAl}.
+           Because this line occurs in such a clean region of the photon spectrum and is so intense,
+           it could possibly be used for monitoring the number of stopped muons
+           in Mu2e and COMET.}
+  \label{fig:xrayanalysis:mg26_1809}
+\end{figure}
+
+A second gamma line at 844 keV results from the beta decay of
+the relatively long-lived (9.5 minutes) $^{27}$Mg isotope
+produced in the reaction
+$^{27}_{13}\mbox{Al}+\mu^-\to\nu_{\mu}+^{27}_{12}\mbox{Mg}$.
+Though counting this peak agreed within error with that expected from published
+branching ratios, the uncertainty is large due to poor statistics.
+By improving the statistics
+under this peak in the proposed run we will
+determine a more precise branching ratio, making it useful as a potential
+normalisation to the number of muon stops in Mu2e and COMET.
+The current data for this peak, as well as nearby peaks,
+is illustrated in figure \ref{fig:xrayanalysis:mg27_844kev}.
+
+\begin{figure}
+  \centering
+  \includegraphics[width=0.5\textwidth]{figs/mg27_844keV}
+  \caption{A peak at 844 keV from the decay of $^{27}_{12}$Mg is
+           correlated with the number of stopped muons in the target.
+           Unfortunately the yield is low and additionally polluted
+           by a nearby iron peak. With the statistics from our first run,
+           we could not determine to a sufficient precision the number
+           of these $\gamma$s we expect per captured muon, however we
+           will be able to achieve this in the proposed next run when the statistics will be much improved.}
+  \label {fig:xrayanalysis:mg27_844kev}
+\end{figure}