The conversion experiment proposes to monitor the number of stopped muons
by measuring the various muonic X-rays generated by the captured muons
as they cascade down to the muonic atom ground state.  We propose to
test this scheme at PSI, as well as two alternate normalization
methods. 

At PSI, we propose to install a high-purity germanium detector at a
port in the stopping target vacuum vessel to measure the rate of
muonic X-ray production and hence the number of muons stopped in the
target. Table \ref{tb:xray_energies} lists the most prevalent gamma
rays from the Si, Al, and Ti targets.   
Typical energy resolution of the HPGe detector will be of order 2~keV
for 1~MeV photons. Normalization of the other measurements in this
proposal will rely on the HPGe detector, although use of an active Si
target will provide a useful cross-check. 

A mechanical cooling system will be provided for the HPGe detector,
eliminating the need for a liquid nitrogen supply, although cooling
with cryogens is still a possibility if the mechanical system is
deemed insufficient.  A high-speed, 14-16 bit data acquisition system
will be used to record and store high-resolution raw waveforms for
offline analysis, although real-time spectra will also be available
for monitoring.  The raw data stream will be provided to the
DAQ systems of the other detectors. 

Measurements of particular interest using the Mu2e germanium detector
include the muonic X-ray and gamma spectra as well as careful analysis
of both immediate and long-term effects of neutron on the detector.
Fast neutrons can create spurious peaks due to excitation of Ge nuclei
through inelastic neutron scattering, background signals from activation
products in both the detector and surrounding cryostat, and long-term
resolution degradation due to creation of hole-trapping defects in the
germanium lattice. The distance between the target and HPGe detector
in the PSI experiment will be selected such that long-term damage to
the HPGe is minimized, although the actual neutron flux is expected to
be small. 

A large NaI detector will be used to measure the high energy photons
from the muon stopping target, with the primary goal of evaluating alternative
means of monitoring the stopped muon rate. Photons from radiative muon
decay have a probability distribution that decreases to nearly zero at
about 54~MeV. The NaI detector has 9 PMTs viewing a large single
crystal, whose signals will be digitized using waveform digitizers and
then fed into the regular DAQ data stream. The rate of photons from
radiative muon capture, ranging up to about 80-90~MeV, will also be
measured. 

\begin{table}[ht!]
\begin{center}
	\caption{Energies of muonic X-rays in selected target elements.}
	\label{tb:xray_energies}
	\vspace{5mm}
	\begin{tabular}{|l|rrr|}
		\hline
		Transition		& Si (keV)	& Al (keV)	& Ti (keV)	\\
		\hline
		$2p \rightarrow 1s$	& 400		& 347		& 1021		\\
		$3p \rightarrow 1s$	& 477		& 413		& 1210		\\
		$4p \rightarrow 1s$	& 504		& 436		& 1277		\\
		$3d \rightarrow 2p$	&  77		&  66		&  189		\\
		\hline
	\end{tabular}
\end{center}
\end{table}
