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Tran \\ Boston University} +\date{\today} +\maketitle + +\begin{abstract} + The goal is study the emission rate of the \SI{1808.7}{\kilo\eV} gamma rays + (from the first excited state of \ce{^{26}Mg}) after nuclear muon capture on + \ce{^{27}Al}. The measured emission rate is \SI{51(5)}{\percent} per muon capture. +\end{abstract} + +\section{Experimental set up} +\label{sec:experimental_set_up} +This measurement is part of the AlCap experiment done at PSI, Switzerland. +The 2015 summer run focused on the detection of neutral particles: low energy +X-ray, gamma ray and neutron emission after the muon is captured by the +nucleus. + +The X-rays and gamma rays of interest are: +\begin{itemize} + \item muonic $2p-1s$ transition in aluminum: \SI{346.8}{\kilo\eV} + \item \SI{843.7}{\kilo\eV} gamma from the $\beta^-$ decay of \ce{^{27}Mg} + (half-life: \SI{9.46}{\min}) + \item \SI{1808.7}{\kilo\eV} gamma from the first excited state of + \ce{^{26}Mg} +\end{itemize} + +Low momentum muons (less than \SI[]{40}{\mega\eVperc}) were stopped in +a target after passing a muon counter +(\SI{60}{\mm}$\times$\SI{60}{\mm}$\times$\SI{0.5}{\mm} plastic scintillator). +% Upstream from the muon counter, a +% \SI{10}{\cm} $\times$ \SI{10}{\cm} $\times$ \SI{0.6}{\cm} scintillator with +% a \SI{40}{\mm} diameter hole cut in the center acted as a beam defining +% veto counter to the incoming muon beam. +There were two 5"$\times$2" liquid scintillator BC501a detectors setup on the +beam right to detect neutrons. For gamma spectrum analysis and normalization +we used an HPGe detector installed on the beam left. In addition, a \ce{LaBr3} +scintillator was also tested if it would be suitable to use in the STM. A 25 +LYSO crystal array was placed downstream of the target beam left to observe +high energy photons emitted. + +Two identical preamplifier outputs from the HPGe detector were fed into: (a) +a timing filter amplifier for timing information, and (b) a spectroscopy +amplifier for energy information. The timing pulses were read out by a 14-bit +500-MS/s desktop digitizer(CAEN DT5730). In order to accommodate both low +energy X-rays and relatively high energy gamma rays, we used two channels from +the spectroscopy amplifier with different gain settings: (a) a lower gain +channel for photons up to \SI{6.5}{\mega\eV}; and (b) a higher gain channel for +photons up to \SI{2.5}{\mega\eV}. These channels were read out by a 14-bit +100-MS/s VME digitizer (CAEN V1724). + +The \ce{LaBr3} crystal is coupled with a photomultiplier, of which output +pulses were large enough so no further amplification was needed. This channel +is read out with the DT5730. + +% Detectors' outputs were read out using waveform digitizers. We used a 14-bit +% 100-MS/s VME digitizer (CAEN V1724) to record energy signals from +% HPGe and \ce{LaBr3} detectors. There were two energy outputs from the HPGe +% detector with different gain settings: (a) low gain channel for photons up to +% \SI{6.5}{\mega\eV}; and (b) high gain channel for photons up to +% \SI{2.5}{\mega\eV}. The timing signals from these detectors, and signals from +% plastic and liquid scintillators were fed into a faster digitizer, namely +% a 14-bit 500-MS/s desktop digitizer (CAEN DT5730). +% These fast timing channels +% were also read out using a multihit TDC (CAEN V1290A) as a back up solution. +% All digitizers and TDC were synchronized by an external master clock. + +Experimental layout is shown in \cref{fig:R2015a_setup}. +\begin{center} + \begin{figure}[!tbp] + \centering + \includegraphics[width=0.70\textwidth]{figs/R2015a_setup_2.jpg} + \caption{Layout of the AlCap 2015 summer run. Muons entered from the top of + the image. The LYSO detector is not visible in this image, which is + located further out in the bottom of the image.} + \label{fig:R2015a_setup} + \end{figure} +\end{center} + +There were several runs with different targets made of aluminum, titanium, +lead, water. All targets were sufficiently thick to stop the muon beam with +momenta up to \SI{40}{\mega\eVperc}. +% Table~\ref{tab:alcap2015a:datasets} summarizes the data +% sets for the main production run and number of muons +% entering the experiment as counted by the beam scintillator counter TSc. Data +% were also collected on stainless steel, tungsten and mylar targets with +% a substantially reduced amount of data collection time. + +\section{Analysis} +\label{sec:analysis} +In this study, the dataset on a \SI{2}{\mm} thick aluminum target is used. It +was collected in 31 hours of beam time and contains about \num{1.91E9} stopped +muons. Momentum of the muon beam was \SI{36}{\mega\eVperc}. + +\subsection{Digital pulse processing} +\label{sub:digital_pulse_processing} +Since we recorded all detector outputs using digitizers, offline digital pulse +processing is needed to extract energy and timing information. Typical output +pulses from HPGe and \ce{LaBr3} detectors are shown in +\cref{fig:typical_pulses}. + +\begin{center} + \begin{figure}[htbp] + \centering + \includegraphics[width=1.0\textwidth]{figs/typical_pulses} + \caption{Typical output pulses of HPGe and \ce{LaBr3} detectors: energy + output HPGe high gain (top left), energy output HPGe low gain (top + right), timing output HPGe (bottom left), and \ce{LaBr3} (bottom right).} + \label{fig:typical_pulses} + \end{figure} +\end{center} + +The timing pulses from the HPGe detector were not used in this analysis because +they are too long and noisy (see bottom left \cref{fig:typical_pulses}). +Energy of the HPGe detector is taken as amplitude of spectroscopy amplifier +outputs, its timing is determined by the clock tick where the trace passing +\SI{30}{\percent} of the amplitude. + +\ce{LaBr3} pulses were passed through a moving average window filter (60 +samples wide), then integrated to obtain energy resolution. + +\subsection{Calibrations} +\label{sub:calibrations} +The HPGe and \ce{LaBr3} detectors acceptance and energy scales were calibrated +using \ce{^{152}Eu}, \ce{^{60}Co}, \ce{^{88}Y} sources placed at the target +position. There was a separate run for background radiation. + +\cref{fig:uncalibrated_labr3_spectra} shows \ce{LaBr3} +spectra with calibration sources \ce{^{88}Y}, \ce{^{60}Co}, and background +radiation. It can be seen that the self activation from \ce{Ac} dominates the +spectra. The \SI{1173}{\kilo\eV} peak barely shows up in \ce{^{60}Co} +spectrum, while the \SI{1332}{\keV} peak is buried under the +\SI{1436}{\kilo\eV} peak from \ce{^{138}La}. The \SI{1836}{\kilo\eV} +peak of \ce{^{88}Y} and the annihilation peak \SI{511}{\kilo\eV} can be +distinguished, but the \SI{898}{\kilo\eV} has been distorted by the electrons +and \SI{789}{\kilo\eV} gammas from the beta decay of \ce{^{138}La}. The energy +resolution (FWHM) at the \SI{1836}{\kilo\eV} peak was \SI{5.9}{\percent}. + +\begin{center} + \begin{figure}[htbp] + \centering + \includegraphics[width=1.0\textwidth]{figs/labr3_spectra_w_gatedintegration} + \caption{Calibration of the \ce{LaBr3} detector, top horizontal axis shows + energy and bottom horizontal axis shows integration of the output pulses. + The spectra were scaled to make the peak recognition easier.} + \label{fig:uncalibrated_labr3_spectra} + \end{figure} +\end{center} + +The HPGe spectra are much cleaner as shown in Figure~\ref{fig:hpge_ecal}. +\begin{center} + \begin{figure}[htbp] + \centering + \includegraphics[width=1.0\textwidth]{figs/hpge_ecal} + \caption{Energy calibration spectra for the HPGe detector.} + \label{fig:hpge_ecal} + \end{figure} +\end{center} +% Energy resolutions were good for all calibration peaks. +The detector acceptance +were fitted as a function of photon energy above \SI{200}{\kilo\eV}: +\begin{equation} + A = c_1 \times E ^ {c_2}, +\end{equation} +where $c_1 = 0.1631$, $c_2 = -0.9257$. Interpolation gives detector acceptance +at the peaks of interest as shown in \cref{tab:hpge_acceptance}. + +\begin{center} + \begin{figure}[htbp] + \centering + \includegraphics[width=1.0\textwidth]{figs/hpge_higain_acceptance} + \caption{Acceptance of the HPGe (high gain channel) as a function of photon + energy.} + \label{fig:hpge_higain_acceptance} + \end{figure} +\end{center} + +\begin{table}[htbp] +\centering +\caption{HPGe acceptance for photons of interest} +\label{tab:hpge_acceptance} +\begin{tabular}{@{}cccc@{}} +\toprule +\multicolumn{2}{c}{\textbf{\begin{tabular}[c]{@{}c@{}}Photon energy\\ {[}keV{]}\end{tabular}}} & \textbf{Acceptance} & \textbf{Error} \\ +\midrule +$2p-1s$ & 346.8 & \num{7.26e-4} &\num{4.73e-5} \\ +% 3p-1s & 399.3 & \num{6.38e-4} &\num{3.71e-5} \\ +% 4p-1s & 400.2 & \num{6.36e-4} &\num{3.70e-5} \\ +% 5p-1s & 476.8 & \num{5.41e-4} &\num{2.72e-5} \\ +\ce{^{27}Mg} & 843.7 & \num{3.19e-4} &\num{1.20e-5} \\ + % & 1014.4 & \num{2.69e-4} &\num{1.07e-5} \\ +\ce{^{26}Mg}* & 1088.7 & \num{1.57e-4} &\num{9.80e-6} \\ +\bottomrule +\end{tabular} +\end{table} + +\section{Results and discussion} +\label{sec:results_and_discussion} + +\subsection{\ce{LaBr3} spectra} +\label{sub:labr3_spectra} +The \ce{LaBr3} energy spectra for the Al dataset are presented in +\cref{fig:labr3_all_al_runs}. The muonic $2p-1s$ peak shows up clearly in +the prompt spectrum as expected. The \SI{1809}{\kilo\eV} peak can be +recognized, it has better +signal-to-background ratio in the prompt spectrum than in the delay spectrum +(0.88 to 0.33). The background under the \SI{1809}{\kilo\eV} is dominated by +the $\alpha$ decay of progenies from \ce{^{227}Ac}. I think that this +\ce{LaBr3} in the current set up is not suitable to use as a STM detector. +\begin{center} + \begin{figure}[htbp] + \centering + \includegraphics[width=1.0\textwidth]{figs/labr3_all_al_runs} + \caption{\ce{LaBr3} spectra: prompt (less than \SI{100}{\ns} from muon + hit), delay ($>$ \SI{100}{\ns} from muon hit), and all hits.} + \label{fig:labr3_all_al_runs} + \end{figure} +\end{center} + +\subsection{HPGe spectrum} +\label{sec:hpge_spectrum} +The HPGe photon spectrum for the aluminum dataset is shown in +\cref{fig:GeCHH_all_al_runs}. Both the \SI{347}{\kilo\eV} +and \SI{1809}{\keV} peaks are clearly visible with the X-ray peak dominates in +the prompt spectrum. The apperance of the \SI{347}{\keV} (and other X-ray +peaks) in the delay spectrum can be explained by a second muon stopped in the +aluminum target shortly after the trigger muon. +\begin{center} + \begin{figure}[htbp] + \centering + \includegraphics[width=1.0\textwidth]{figs/GeCHH_all_al_runs} + \caption{HPGe high gain spectra: prompt (less than \SI{500}{\ns} from muon + hit), delay ($>$ \SI{500}{\ns} from muon hit), and all hits.} + \label{fig:GeCHH_all_al_runs} + \end{figure} +\end{center} + +\subsection{Number of stopped muons} +\label{sub:number_of_stopped_muons} + +The number of stopped muons is calculated by two methods: +\begin{itemize} + \item infering from the number of $2p-1s$ X-rays, + \item counting the muon hits on the muon counter. +\end{itemize} +The latter gives the number of stopped muons as: +\begin{equation} + N_{\mu} = 3.03 \times 10^8 \pm 1.7 \times 10^4. + \label{eqn:n_mu_TSc} +\end{equation} + +The number of $2p-1s$ X-rays is calculated by fitting a Gaussian peak with +a linear background to the region \SIrange{340}{350}{\keV} around the peak in +the prompt HPGe spectrum: +\begin{equation} + N_{346.8} = (191.27 \pm 0.42) \times 10^3. +\end{equation} +Using the acceptance of the $2p-1s$ photons in \cref{tab:hpge_acceptance}, +number of stopped muons is: +\begin{equation} +N_{\mu} = \frac{N_{346.8}}{A_{346.8}} = (3.30 \pm 0.22) \times 10^8, +\end{equation} +which is consistent with that in \cref{eqn:n_mu_TSc}. + +\subsection{Emission rate of \SI{1809}{\keV} photons} +\label{sub:emission_rate_of_1809_kev_photons} +Number of the \SI{1809}{\keV} photons is calculated using the same method for +the \SI{347}{\keV} photons: +\begin{equation} + N_{1808.7} = 16032.54 \pm 166.19. +\end{equation} +Therefore the emission rate per nuclear capture is: +\begin{equation} + R_{1808.7} = \frac{N_{1808.7}}{A_{1808.7} \times N_{\mu} \times 0.609} = 0.51 \pm 0.05, +\end{equation} +, where the factor 0.609 comes from the fact that only \SI{60.9}{\percent} of +stopped muons are captured. This result is consistent with the rate reported +by Measday et al. + +\end{document}