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\article{WG4}{SINDRUM II}
\author{Andries van der Schaaf}
\address{Physik-Institut der Universit\"at Z\"urich, Switzerland}
\ead{andries@physik.unizh.ch}

\begin{abstract}
In the year 2000 {\sf SINDRUM II} took final data in a search for
$\mu$e conversion on gold. A short description of the experiment and some
preliminary results are presented.
\end{abstract}

\pacs{11.30.Fs 11.30.Hv 13.35.Bv 13.60.-r 14.60.Ef}
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\section{Introduction}
The conversion $\mu \to e$ of a $\mu^-$ bound in a muonic atom is a sensitive
test of charged lepton flavour conservation \cite{avdsplenary}. In the past
decade in a series of searches with the {\sf SINDRUM II} spectrometer limits on
the conversion rates on medium and heavy nuclei have improved significantly.
This program was finished in the year 2000 with a measurement on gold. See
\cite{avdsplenary} for a general discussion of $\mu$e conversion experiments
and the {\sf SINDRUM II} gold run in particular. Here I will discuss some more
details.

\section{The {\sf SINDRUM II} spectrometer}
\begin{figure}[h]
\begin{center}
\includegraphics[height=45mm]{r87-03-fig1.eps}
\end{center}
\caption{\label{figlabel1}The {\sf SINDRUM II} spectrometer}
\end{figure}
Figure~\ref{figlabel1} shows a vertical cross section through the spectrometer
in the configuration used in the year 2000. Typical trajectories of a beam
$\mu^-$ and a hypothetical conversion electron are indicated. 

\section{$\pi-\mu$ separation}
Radiative $\pi^-$ capture followed by $\gamma \to e^+e^-$ produces electrons
with energies in the region of interest with a probability of $O(10^{-5})$ (see
also section~\ref{spectra} below). Such prompt beam related background can be
suppressed by beam pulsing, a beam veto counter, or beam purity. For heavy
muonic atoms with lifetimes below 100~ns the first two methods lead to large
inefficiencies. Here pions are removed with the help of an 8~mm
thick CH$_2$ degrader at the entrance of a 9~m long solenoid which is coupled
directly to the spectrometer (see figure~\ref{figlabel1} and
\cite{avdsplenary}). At 50~MeV/c $\pi^-$ stop in the degrader and $\mu^-$ go
through (see figure~\ref{figlabel2}).
\begin{figure}[h]
\includegraphics[width=0.57\linewidth]{pi_mu_straggling.eps}\hspace*{\fill}
\includegraphics[width=0.35\linewidth]{26mev.eps}
\caption{\label{figlabel2}Left: CH$_2$ crossing probability calculated for
50~MeV/c $\pi^-$ and $\mu^-$ v.s. thickness. Right: experimental $\mu^-$
crossing probabilities before and after optimisation. The latter were monitored
through their decay electrons. The beam momentum was reduced for better $\mu^-$
identification.}
\end{figure}
The tails in the calculated distributions result from range straggling. In
practice the range
distributions depend mainly on the momentum distribution of the
beam. By carefully adjusting the fields in the various beam elements the
required steeply falling range distribution was obtained.

\section{Number of $\mu$ stops}
Target stops were monitored by observing
\begin{figure}[h]
\begin{center}
\includegraphics[height=33mm]{au2000exp.ps}
\end{center}
\caption{\label{figlabel3}X-ray spectrum accumulated during three hours of
$\mu$e data taking.}
\end{figure}
muonic X-rays with a Ge(Li) detector positioned outside
the spectrometer coil (see figure~\ref{figlabel3}). Detector efficiency and
acceptance were calibrated with radioactive sources. The number of $\mu^-$
stopping in the gold target during $\mu$e data taking determined this way was
$4.3 \pm 0.2 \times 10^{13}$.  

\section{Momentum spectra}
Figure~\ref{figlabel4} shows momentum spectra observed with the spectrometer
for various settings of the beamline. Events were selected with trajectories
\label{spectra}
\begin{figure}[h]
\begin{center}
\includegraphics[height=80mm]{r87-03-fig2.eps}
\end{center}
\caption{\label{figlabel4}Momentum distributions for three different beam
momenta and polarities: (i) 53~MeV/c negative optimized for $\mu^-$ stops,
(ii) 63~MeV/c negative optimized for $\pi^-$ stops, (iii) 48~MeV/c positive
optimized for $\mu^+$ stops. The 63~MeV/c data were normalized to correct for
the different measuring times. The $\mu^+$ data were taken at scaled
spectrometer field.}
\end{figure}
originating in the target and cosmic background was suppressed as discussed in
\cite{avdsplenary}. The main spectrum taken at 53~MeV/c shows the steeply
falling distribution expected from muon decay in orbit
$\mu^-$Au$\to e^- \nu \overline{\nu}$Au. Two events are observed at higher
momenta just outside the region of interest. The agreement between measured
and simulated spectra for $\mu^+$ decay gives confidence in the momentum
calibration.

\section{Single-event sensitivity}
The total efficiency for observing a $\mu$e conversion event including the
geometrical acceptance and the efficiencies of the detector, the trigger for
readout and the event reconstruction and selection amounts to $7\pm 1$\%.
This corresponds to a single-event sensitivity of $3.3\pm0.3\times10^{-13}$,
i.e. almost two orders of magnitude below the best previous result on a heavy
target \cite{snd2a}. We expect to produce the corresponding 90\% c.l. upper
limit on the branching ratio before the end of 2002.

\section*{References}
\begin{thebibliography}{99}
\bibitem{avdsplenary}     van der Schaaf A 2003
Muon Physics {\it Proc. Nufact'02 (London)}

\bibitem{snd2a}           Kaulard J \etal {\sf SINDRUM II} Collaboration 1998
\PL B {\bf 422} 334--38


\end{thebibliography}
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