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