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AlCapPSI/Protons.tex
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AlCapPSI/Protons.tex
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The goal of the experiment is a measurement of the rates and energy spectra of
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charged particle emission after muon capture in; 1) the favored
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conversion target,
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Al, 2) in Si (as normalization and cross check), and 3) Ti (as an alternative
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conversion target material). Both the rate and energy spectrum
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would be measured at
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5\% precision down to an energy of 2.5 MeV.
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The basic requirements are summarized is Fig.~\ref{basic.fig}. As the emitted
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charged particles deposit a significant amount of energy during their passage
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through the target material, thin targets and thus excellent momentum
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resolution of the low energy muon beam are critical for the experiment. This
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is exactly the reason, why the older experiments, which were performed
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with thick targets and less sophisticated beams, are unsuitable for providing
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the required yield and spectral information at low energies.
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The observed energy spectrum $g(T_f)$ of protons emitted from the stopping
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target is a convolution of the initial capture spectrum $f(T_i)$ with a
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response function $k(T_f,T_i)$:
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\begin{equation}
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g(T_f) = \int_0^\infty k(T_f,T_i) f(T_i) dT_i
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\end{equation}
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The response function can be readily calculated for a uniform muon stopping
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distribution within the target depth. The resulting distortion of the original
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energy distribution taken from Equ.~\ref{eq:protons} is illustrated in
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Fig.~\ref{response.fig} for different target thickness.
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\begin{figure}[htb]
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\begin{center}
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\includegraphics[width=\textwidth]{figs/protonrange.png}
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\caption{Left: Momentum vs. energy for p, d, $\alpha$,
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right: proton range
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vs. energy in targets.}
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\label{basic.fig}
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\end{center}
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\end{figure}
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%\vskip-5ex
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\begin{figure}[tb]
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\begin{center}
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\includegraphics[width=0.6\textwidth]{figs/Si_emitted.pdf}
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\caption{Calculated proton emission spectrum as
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function of target
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thickness (red: 0 $\mu m$, green: 50 $\mu m$, blue:
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100 $\mu m$, black :
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1000 $\mu m$).}
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\label{response.fig}
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\end{center}
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\end{figure}
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\begin{figure}[tb]
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\begin{center}
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\includegraphics[width=0.39\textwidth]{figs/expcad.png}\hspace{1mm}\includegraphics[width=0.59\textwidth]{figs/exp.png}
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\caption{Left: CAD of layout, right: picture of vacuum
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vessel with detectors.}
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\label{setup.fig}
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\end{center}
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\end{figure}
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A schematic layout of the experimental setup is shown in Fig.~\ref{setup.fig}.
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It will be an improved version of a test experiment performed by part of this
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collaboration at PSI in 2009.
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Low energy muons will be detected by external beam counters (scintillator and
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wire chamber, not shown). The muons then enter a vacuum vessel though
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a thin mylar
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window and a fraction stopped in passive Al and Ti foils of 25 to 100 $\mu m$
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thickness. These foils are aligned 45 degrees with respect to the
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beam direction. As a cross check, muons
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will also be stopped in active Si detectors used as targets. Two packages
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of charged particle detectors are positioned on opposite sides, perpendicular
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to the target surface. The geometry is chosen so as to minimize the path length
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of the emitted protons, and limit their direction to be nearly perpendicular to
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the detectors. This improves the PID resolution by dE/dx separation. The main
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detector of the package is a 5$\times$5 cm$^2$ Si detector of 1500 $\mu m$
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thickness (MSX), which will stop protons up to about 12 MeV. Plastic
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scintillators positioned
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behind this Si detector observe higher energy protons and veto
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through-going electrons. To provide dE/dx information some data will be taken
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with two 10x10 cm$^2$ thin Si detectors (65 $\mu m$, MSQ). These detectors are
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4-fold segmented. Since their large capacitance deteriorates the overall
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resolution, measurements with and without them are foreseen. The symmetry
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between the left and right Si stations allows for a powerful monitor of
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systematic effects. Differences between the detectors would indicate background
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due to different stopping materials, non--uniform stopping distributions, or
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differences due to muon scattering. Careful shielding of direct or scattered
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muons is required, as the stopping fraction is small and proton emission is a
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rare capture branch. As shown, we are considering a geometry, where there is no
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direct line of sight between any low Z material exposed to muons. Thus, all
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shielding uses lead.
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In order to normalize the number of muon-stops in the aluminum target, a
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Germanium detector will be used to measure muonic X-rays from muons
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that stop in the aluminum
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target. We also will have telescopes to detect electrons from
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muons for an additional normalization of muon-stops.
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The main systematic issues are as follows.
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\begin{itemize}
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\item Deconvolute the original proton spectrum $f(T_i)$. An optimal
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cloud muon beam is requested for the experiment. Then an active
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Si target allows an experimental calibration of the response function,
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because both $T_i$ and $T_f$ are accessible with an active target.
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\item Absolute calibration. The number of muon stops will be determined with
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the Ge detector. Again, the use of an active Si target allows a cross
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calibration. The proton detection efficiency will be simulated
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by Geant and calibrated with the active Si target.
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\item PID. The PID of emitted charged particles will be determined by dE/dx.
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The use of time of flight will be investigated.
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\item Background. Electron background will be determined with $\mu^+$, neutron
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recoils by absorbing the proton component before the Si detectors. A
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dangerous background are muons stops in walls and scattered into the Si
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detector.\footnote{If the low energy target scattering is too
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high, we are also studying a configuration, with the two Si
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detectors positioned symmetrically and perpendicular to the beam.}
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\end{itemize}
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A realistic Geant4 simulation is being developed. It will serve as an important
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tool to optimize the geometry, in particular the investigation of the
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background and response
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function. Currently the geometry of the PSI test run is being implemented for a
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realistic check of the simulation.
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\begin{figure}[htb]
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\begin{center}
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\includegraphics[width=0.8\textwidth]{figs/dEdx_new.pdf}
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\caption{Two dimensional plots of energy deposit in
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Si1 (65 $\mu$m) vs sum of that in Si1 (65 $\mu$m) and Si2 (1500$\mu$m)
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(horizontal) counters. The protons can be distinguished from
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deuterons and
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tritons in the range of 2.5 $-$ 10
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MeV. The low energy particles near zero point are electrons
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and photons.}
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\label{fg:dedx}
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\end{center}
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\end{figure}
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\begin{table}[htb]
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\begin{center}
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\caption{
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\label{tb:rates} Estimated event rates for various targets of different
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thickness. Incoming $10^{4}$ muons/sec and proton
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emission rate of
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0.15 per muon capture are assumed. The efficiency of
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Si detector of
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100 \% is also assumed. \label{tb:rates} }
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\vskip1ex
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%\scalebox{0.75}{
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\begin{tabular}{|c|c|c|c|c|}
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\hline
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Target & Muon momentum &\% Stopping & Event rate (Hz) & Event rate (Hz) \\
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thickness ($\mu$m)& (MeV/c) &in target & All particles
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& Protons \\
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\hline
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50 & 26 & 22.2 & 34.8 & 4.6 \\
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100 & 27 & 32.9 & 48.5 & 5.4 \\
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150 & 28 & 38.5 & 54.5 & 4.8 \\
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200 & 28 & 51.2 & 47.7 & 4.5 \\
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%50 & 26 & 22.2 & 14.8 & 2.3 \\
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%100 & 27 & 32.9 & 18.5 & 2.1 \\
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%150 & 28 & 38.5 & 16.6 & 1.7 \\
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%200 & 28 & 51.2 & 19.8 & 2.0 \\
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\hline
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\end{tabular}
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%}
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\end{center}
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\end{table}
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Figure~\ref{fg:dedx} shows Monte Carlo simulation studies of two-dimensional
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plots of energy in the MSQ counter (dE/dX) vs. energy of the MSX counter. From
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Fig.~\ref{fg:dedx}, it is clearly seen that we can discriminate protons,
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deuterons, scattered muons, and electrons up to 10 MeV.
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The event rates are estimated based on Monte Carlo simulation. Preliminary
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results are summarized in Table~\ref{tb:rates}. They will be updated once we
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have full information about the PSI beam properties. As seen in
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Table~\ref{tb:rates}, proton rates are not large. Additional collimation,
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if required to obtain background reduction, and the low muon momenta,
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which might require the use of degraders, may further reduce the rates
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below these estimates.
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A muon beam
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of low and well defined momentum is of critical importance.
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