A neutrino and a charged lepton form a natural doublet in the SM, and
are assigned a flavor quantum number. The
observation that neutrinos oscillate between flavours and thus have
mass, means that lepton number is not absolutely conserved in the
neutral lepton sector and this in
turn means that lepton number is also not conserved in charged lepton
interactions. However, due to the large difference in mass between the
neutrino and the $W$ boson, the branching ratio for charged lepton
flavour violation (CLFV) in a minimal extension to the SM which
includes massive neutrinos, is extremely small
(${\cal{O}}(10^{-50})$). Thus, any experimental observation of CLFV would be
unambiguous evidence of new physics beyond the SM (BSM), and 
particle physics experiments searching for CLFV are amongst those with
highest priority ~\cite{Kuno:1999jp}. 

Most extensions to the SM predict rates for CLFV that are within reach
of the next generation of experiments. Indeed current experiments such
as MEG search for the CLFV process, $\mu^{+} \rightarrow
e^{+}\gamma$, and already place severe constraints on models of BSM
physics. It is possible to construct a generic Lagrangian for BSM CLFV
interactions~\cite{deGouvea} comprising dipole and
contact interaction terms at a certain mass scale
($\Lambda$). The $\mu^{+} \rightarrow e^{+}\gamma$ being probed by MEG,
is mainly sensitive to dipole interactions whereas processes such as
$\mu^{+} \rightarrow e^{+}e^{-}e^{+}$ and the coherent neutrinoless
transition of a muon in the field of a nucleus, \muec, are mainly
sensitive to contact interactions. Thus in order to elucidate the
nature of any BSM physics it is necessary to make measurements of all
three processes. In Fig.~\ref{fg:deGouvea} the rates of CLFV are shown
as a function of $\Lambda$ and the relative contribution of the dipole
and contact interactions ($\kappa$).  
 
\begin{center} 
\begin{figure}[htbp]
\hspace{30mm}
\includegraphics[width=0.6\textwidth]{figs/deGouvea.png}
\caption{Branching ratios for two CLFV processes in a generic model of
BSM physics having both dipole and contact interactions as a function
of the scale ($\Lambda$) of the new physics.} 
\label{fg:deGouvea}
%\vspace{-5mm}
\end{figure}
\end{center}

It can be seen from Fig.~\ref{fg:deGouvea} that CLFV processes
potentially probe new physics at scales beyond the LHC. Dipole and
contact interactions arise in many models of BSM
physics. Supersymmetric interactions naturally provide dipole
interactions which could result in significant rates for both the
$\mu^{+} \rightarrow e^{+}\gamma$ and \muec processes while  
contact interaction terms arise in type-II Seesaw models that generate
light neutrino masses through mixing with an additional massive
neutrino. In general the Seesaw mechanism occurs at a very high mass scales
(${\cal{O}}(10^{10-14})$~GeV). CLFV effects are only large if
additional new physics e.g. supersymmetry or extra dimensions are
present at the TeV scale.  In general CLFV processes probe
physics both at the GUT-scale and the
TeV-scale. Fig.~\ref{fg:deGouvea} also highlights the necessity of
searching for CLFV in both the $\mu^{+} \rightarrow e^{+}\gamma$ and
\muec process (and also the $\mu^{+} \rightarrow e^{+}e^{-}e^{+}$
process) where the ratio of the branching ratios can yield information
on $\kappa$. 

The last search for \muec conversion was performed by the SINDRUM
II collaboration at PSI.  The SINDRUM II spectrometer consisted of a
set of concentric cylindrical drift chambers inside a superconducting
solenoid magnet of 1.2 Tesla. The experiment set an upper limit of \muec in Au
of $B(\mu^{-} + Au \rightarrow e^{-} + Au) < 7 \times
10^{-13}$~\cite{SindrumGold}. Two new searches for 
CLFV in the \muec process are being pursued by
experiments under construction in the USA (Mu2e~\cite{mu2e08}) and
Japan (COMET~\cite{come07}), both of which seek to probe the
\muec process with a sensitivity better than $\sim
10^{-16}$. Schematic layouts of the experiments are shown in
Fig.~\ref{fg:mu2ecomet}. For BSM interactions dominated by dipole
operators these experiments have a similar sensitivity to the upgraded
MEG experiment but have a far greater sensitivity to contact
interactions. 

The Mu2e and COMET experiments are seeking to improve on the SINDRUM
II sensitivity by a factor of 10,000. Both experiments utilise
multi-kW pulsed proton beams of energy 8--9~GeV produced by the FNAL
(Mu2e) and J-PARC (COMET) accelerator complexes. Mu2e received CD1 DOE
approval in July 2012 and the staged construction of COMET was
approved in March 2012 and construction of the beamline will begin in
2013. In the Phase-I COMET experiment, shown in Fig.~\ref{fg:phase1},
there is a reduced beamline and a cylindrical drift chamber will
immediately surround the target where the muons are captured.  Thus, it is
very sensitive to the products of muon (and pion) nuclear capture. In
Mu2e there is a similar sensitivity since the straw tracking detector
is immediately downstream of the muon target. 

\begin{center} 
\begin{figure}[h]
%\vspace{-40mm}
\includegraphics[width=\textwidth]{figs/comet-mu2e.png}
\caption{Schematic layouts of the Mu2e (left) and the COMET Phase-II experiments (right).}
\label{fg:mu2ecomet}
%\vspace{-5mm}
\end{figure}
\end{center} 

 The $\mu^{-}N \rightarrow e^{-}N$ process is particularly
attractive since the experimental signature is very straightforward: a
single mono-energetic electron with an energy of approximately $m_\mu
- B$ where $B$ is the binding energy of the muon in the 1{\em s} level
in the muonic atom (N). This single particle signature does not suffer
from the accidental background which occurs when coincidences are
required; e.g. between $e^{+}$ and $\gamma$ in the $\mu^{+} \rightarrow
e^{+}\gamma$ process.  This is a particularly important, limiting 
background at 
high muon rates. The energy of the mono-energetic electron from the \muec
process has far higher energy than in Michel decays, and for $\mu$
decays in orbit (DIO) the phase space for electron energies
approaching the endpoint rapidly vanishes. 

In addition to the DIO process or the CLFV process a muon in the 1{\em
s} state in a muonic atom can be captured by the nucleus  via the
process: $\mu^{-} + N(A,Z) \rightarrow \nu_{\mu} + N(A,Z-1)$. In
general this process is also accompanied by the emission of photons,
neutrons and charged particles (particularly protons) and it is the
measurement of these emitted particles that is the subject of this
proposal. In order to optimize $\mu \to e$ experiments, it is important
to accurately know the rate and energy spectra of these particles, 
since they can form significant backgrounds, degrade the
efficiency of electron tracking, and damage the readout electronics. 
Photons can Compton scatter or convert, 
producing electrons which cause ambiguities in track reconstruction
and degrade detector resolutions. In addition to these problems, low
energy protons can
saturate the electronic amplifiers due to large energy losses, and
prematurely ``age'' detector components.
Neutrons cause recoil protons and can get captured,
producing photons.  Low-energy neutron cross sections are large and
are difficult to shield. They can cause significant radiation damage.  
Monte-Carlo simulations of these nuclear
capture processes  rely on spectra
data taken over twenty years ago for a limited number of nuclei in
a restricted energy range. Low energy energy neutron spectra are
particularly dependent on the nucleus. The
motivation for this proposal is to make precision measurements for the
target materials that will be used by Mu2e and COMET over the entire
relevant energy region.  





\begin{center} 
\begin{figure}[htbp]
\hspace{15mm}
\includegraphics[width=0.8\textwidth]{figs/comet_phase1_tracker.pdf}
\caption{The COMET Phase-I detector where a cylindrical drift chamber immediately surrounds the muon stopping target and is therefore subject to the products of the nuclear muon capture process.}
\label{fg:phase1}
%\vspace{-5mm}
\end{figure}
\end{center}