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For the proposed run, we plan two types of photon measurements.
%\begin{enumerate}
%\item Measurement of the low energy ($<7$ MeV) gamma and muonic X-ray
% spectra produced when muons stop in candidate target materials, using
% a high resolution germanium detector (FWHM $\sim2$ keV).
%\item Measurement of the high energy photon and electron spectra ($E>30$ MeV)
% produced when muons stop in candidate materials, using $5\times5$
% LSYO-crystal calorimeter array.
%\end{enumerate}
\subsubsection{Low energy ($E<7$ MeV) photons}
Using a high resolution germanium detector we will measure the number of
muonic X-rays emitted from the AlCap targets and will investigate
nuclear gammas emitted in muon capture, as an alternative method to
normalize the number of stopped muons in the Mu2e/COMET experiments.
The emphasis of the first AlCap run (R2013) was to measure the proton
emission spectra on aluminium and silicon targets, which
required placing very thin targets in a vacuum along with the
silicon surface detectors. The setup was excellent for proton measurements
but was not optimal for the measurement of
gammas. A significant fraction of the muon beam stopped in the lead collimator
and other materials located inside the vacuum just upstream of the target,
which led to background in the gamma spectra, for example from
muon capture on lead.
In the proposed upcoming run, we will eliminate the vacuum chamber and
any lead near the muon beam, and place an isolated target in air.
The target would be made sufficiently thick to stop muons at 40 \si{
MeV\per\cc}, which will provide a much higher stopping rate.
%The proposed run would use a muon beam with higher momentum
%than the 29 \si{MeV\per\cc} used for the thin target runs where the stopping
%flux is much higher.
Since all incoming muons will stop in the target,
backgrounds due to stops in shielding material will be significantly reduced.
We also plan add shielding around the Ge detector to add
protection from ambient radiation background.
\paragraph{Aluminium}
%We first discuss the specific case of aluminium.
The number of \atrn{2p}{1s} muonic X-ray transitions per stopped muon is
experimentally determined to be 79(1)\% in aluminium (from the literature).
%The measurement of this rate
%with a high resolution germanium detector provides
%the normalisation for the number of stopped muons in AlCap.
In principle these X-rays can be used to monitor the number of stopped
muons in the Mu2e/COMET experiments. In practice, it remains a
significant challenge for Mu2e/COMET to measure the X-rays. Both Mu2e and
COMET will employ intense pulsed proton and thus pulsed muon beams.
A background in the form of an intense pulse of low energy beam
electrons arrives at the target less
than 100~ns before the muons stop, and produce a ``flash''
of low energy bremsstrahlung. The commercial germanium detectors will
be saturated by the high rates of gammas produced in the flash,
and will not recover in time to measure the X-rays.
Commercially available scintillating crystals are capable of handling much
higher rates but have about x10 poorer resolution (LaBr3(Ce)~3\% at 662~keV)
when compared to Ge.
%In AlCap R2013, thanks to the excellent energy resolution of
%the germanium, we were able to distinguish between the \atrn{2p}{1s} line and a
%nearby background peak due to muons stopping in lead.
In the proposed 2015
run, we will have a thick target without lead shielding. Thus we can evaluate
whether the energy regions near the \atrn{2p}{1s} X-rays are
sufficiently free of
background peaks and noise to permit the use of a faster but lower energy resolution crystal, such as LaBr3, instead of
germanium in the Mu2e/COMET experiments.
Given the challenge of measuring the X-rays for normalisation in Mu2e/COMET,
AlCap will investigate alternatives.
One scenario for Mu2e would be to use a gamma ray from the decay of a nucleus
produced promptly during muon capture. When a muon captures on Al,
it produces $^{27}$Mg about 10-15\% of the time, via the reaction
$\mu^-+ {}^{27}_{13}\mbox{Al}\rightarrow {}^{27}_{13}\mbox{Mg}^*+\nu_{\mu}$. The $^{27}$Mg decays
with a 9.5 minute half-life, emitting an 844 keV gamma 72\% of the time.
(See section \ref{sec:XRayAnalysis} for analysis of this peak in R2013.)
In Mu2e, the beam cycle is such that proton pulses arrive for 0.4 s,
followed by no beam for 0.9 s. A beam shutter would close to protect
the gamma detector (germanium is the likely candidate) from high rates
and radiation damage during beam on,
then it would open during the beam off, when the 844 keV gammas
would be detected.
%In Run 1, we found evidence of the presence
%of the 844 keV peak, however the background was large and we were not able
%to approach the goal of 10\% uncertainty in the number of 844 keV gammas
%per muon stop.
In the proposed 2015 ALCap run, we plan to measure the 844 keV
gammas with 10\% uncertainty.
This measurement will be done with a thick target in air with a minimum
of material near the stopping target. This should
allow us to dramatically increase the stopped muon rate compared to R2013.
We estimate it can be done in one 36 hour measurement.
At the same time, we will study another Mu2e/COMET normalisation alternative,
the use of a 1.8~MeV gamma that is emitted promptly when the muon is captured
on the aluminium nucleus. The gamma is therefore emitted with the lifetime of the muonic
aluminium atom, 864~ns. The gamma ray comes from the chain
$\mu^- + {}^{27}_{13}\mbox{Al}\rightarrow {}^{26}_{12}\mbox{Mg}^*+n+\nu_{\mu}$ followed by the
prompt decay $^{26}_{12}\mbox{Mg}^* \rightarrow {}^{26}_{12}\mbox{Mg}+\gamma$. This gamma is
produced in 50\% of captures.
Detection of the 1.8~MeV~gamma with germanium will be much easier than detecting
the X-rays, since with the Mu2e/COMET pulsed proton beams
it can be delayed 500~ns or more after the proton pulse.
The gamma detector would have to be designed to recover from the 'flash’ in
about 500~ns, and preliminary indications are that this is feasible for
germanium.
If the gamma detector requires a longer time to recover, the measurement
could be delayed more, with the limit being the time of the next proton
pulse 1700~ns later.
\paragraph{Titanium}
Though aluminium is the likely target for Mu2e/COMET,
titanium is an alternate that must be similarly characterised.
The additional task of establishing the $2p\to 1s$ rate per stopped muon
is necessary since this has not been previously
measured, though the
relative intensities of the Lyman and Balmer lines are known~\cite{Kessler:1967}.
A collection of candidate delayed gamma rays from activated nuclei
after capture are appealing for the same reasons as mentioned above for
aluminium. The most interesting come from the capture daughters $^{48}$Sc (44 hours)
and $^{46}$Sc(84 days); both have a yield comparable to
the similar reaction yielding
$^{27}$Mg in aluminium, but emit four gammas with near 100\% intensity.
The gamma rays are
listed in Table \ref{tab:gammas:tidelayed}. The long lifetime of the $^{46}$Sc precludes seeing its decay gammas at AlCap,
however it is of potential use in the much longer-running Mu2e and
COMET experiments and is therefore included here for completeness.
Because of the number of peaks
and their intensities, a measurement time comparable to that planned
for the $^{27}$Mg peak with the aluminium target, 1.5 days,
will be enough to get the necessary statistics
on the $^{48}$Sc peaks.
Observing gamma rays emitted promptly following muon capture also
appears possible.
There are four of interest with intensities of the order 10\% and these are
listed in Table~\ref{tab:gammas:tipromptcapture}. Note that there are other
possible measurements to make, but surveying the literature leads us to
believe the candidates discussed here are the most promising.
\begin{table}
\centering
\caption{After muon nuclear capture in titanium, activated scandium
is produced. One of these has a lifetime much longer than any
measurement time
scales on AlCap, making detecting these gammas impractical. Gammas from
the shorter
lifetime isotope however can be measured in AlCap.
Signature $\gamma$s are produced upon
decay that may prove useful for normalisation in both AlCap and
Mu2e/COMET. Branching ratios after capture~\cite{Evans:1973} refer to how often the isotope is
produced per muon capture. Intensities refer to how often the
$\gamma$ is emitted after the isotope decays.}
\begin{tabular}{c c c c c}
\addlinespace
\toprule
\bf Capture Product & \bf Branching Ratio & \bf Lifetime & \bf Energy & \bf Intensity \\
\bf Isotope & \bf (\%) & & \bf (keV) & \bf (\%) \\
\midrule
$^{48}$Sc & 11.1(9) & 43.7 h & \phantom{1}983.52 & 100\phantom{.0} \\
& & & 1037.6\phantom{0} & \phantom{1}97.6 \\
& & & 1312.1\phantom{0} & 100\phantom{.0} \\
\addlinespace
$^{46}$Sc & 8.1(10) & 83.8 d & \phantom{1}889.28 & 100\phantom{.0} \\
& & & 1120.5\phantom{0} & 100\phantom{.0} \\
\bottomrule
\end{tabular}
\label{tab:gammas:tidelayed}
\bigskip
\caption{(Excerpt of table in \cite{Evans:1973}.) Gammas that are produced
promptly when a muon nuclear captures
on titanium. The intensity is in terms of per-$\mu$-capture.
A number of promising $\gamma$s are given off that may be useful for
normalisation in AlCap and Mu2e/COMET.}
\begin{tabular}{c c c}
\addlinespace
\toprule
\bf Resultant Isotope & \bf Energy (keV) & \bf Intensity (\%)\\
\midrule
$^{48}$Sc & 121.41(4) & 10.5(9)\phantom{1} \\
& 130.94(4) & 10.4(9)\phantom{1} \\
& 370.29(5) & 12.2(8)\phantom{1} \\
\addlinespace
$^{47}$Sc & 807.79(8) & 13.0(15) \\
\bottomrule
\end{tabular}
\label{tab:gammas:tipromptcapture}
\end{table}
Simulations have been done to confirm which lines will be prominent enough to be useful.
By overlaying the simulated peaks onto real Al data (which contains a relevant
sample of background gamma lines),
it is obvious where certain problems will
arise when trying to count these peaks. The X-rays are shown in Figure
\ref{fig:gammas:ti_xrays}, and already we see a lead X-ray may prove
problematic without
proper shielding setup. The $\gamma$s prompt with muon nuclear capture
are in Figure
\ref{fig:gammas:ti_semiprompt} and those from the decay of activated capture
daughters
are in Figure \ref{fig:gammas:ti_delayed}.
Though the poor statistics associated with the R2013 data set
and signal-to-noise
ratio may seem discouraging, with the planned much
improved background suppression
and stopping rates
we expect these peaks to be seen solidly above background in the proposed
AlCap run in 2015.
\begin{figure}
\centering
\includegraphics[width=1.\linewidth]{figs/ti_xray}
\caption{The simulated Ti X-rays (black) were filled over the Al100 data.
Assuming the same number of muon stops as in the data and 100\%
$2p\to1s$ intensity, we see
for the most part the X-rays are readily identifiable. The first
Lyman line, however, would be much easier seen
were it not for the muonic lead X-ray immediately to the left.}
\label{fig:gammas:ti_xrays}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=1.\linewidth]{figs/ti_semiprompt}
\caption{Similar to figure \ref{fig:gammas:ti_xrays}, except
above the simulated Ti signals are $\gamma$s prompt
with muonic nuclear capture. Clearly the signal-to-noise
ratio is poor, though we are confident our improvements in
the next AlCap run will allow these peaks to stand out.}
\label{fig:gammas:ti_semiprompt}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=1.\linewidth]{figs/ti_delayed}
\caption{Similar to figures \ref{fig:gammas:ti_xrays} and
\ref{fig:gammas:ti_semiprompt}, except above are the $\gamma$s from
the decay of the product isotopes after muon nuclear capture in Ti
($^{48}$Sc and $^{46}$Sc)
This plot has assumed each isotope is in equilibrium with the beam,
which can only be achieved with beam on time
equivalent to the isotope's lifetime. Therefore the gammas from
the decay of $^{46}$Sc, with an 84 day half life, will not be visible in AlCap,
however the $^{48}$Sc (44 hours) decays are expected to be visible with a 1.5 day run.}
\label{fig:gammas:ti_delayed}
\end{figure}
\paragraph{Backgrounds}
Finally, it is important to understand the background lines that may exist
in the final Mu2e and COMET experiments. In AlCap Run 1 an unexpected gamma
peak from muons stopping in the stainless steel (SS) chamber appeared very
close to the \atrn{2p}{1s} aluminium X-ray of interest.
By directly measuring, in AlCap, the X-rays and gammas produced by muons
stopping in material that will be abundant in Mu2e/COMET, we can get ahead
of these issues early on.
\subsubsection{High Energy ($E>10$ MeV) Photons and Electrons}
The INFN Frascati group will provide a LYSO calorimeter array in order to
measure higher energy photons and electrons. It will operate parasitically
with a stand-alone DAQ, during the proposed thick target runs when the
neutrons and low-energy gammas will also be measured.
The array consists of LYSO crystals
with dimensions $3 \times 3 \times 13~\textrm{cm}$ in a $5\times5$ array, read out with $1 \times 1~\textrm{cm}$
Hamamatsu APDs and waveform digitisers.
The high energy photons will include those from radiative muon capture (RMC)
and from
radiative muon decay.
RMC is expected to dominate above about 80 MeV.
(See Figure \ref{fig:RMC-RMD-DIO})
\begin{figure}
\centering
\includegraphics[width=0.5\textwidth]{figs/RMC-RMD-DIO.jpg}
\caption{Simulated energy spectra of electrons and photons emitted from
muonic aluminium. Electron spectrum from muon decay in orbit
(red). Photon spectrum from radiative muon capture
(blue). Photon spectrum from radiative muon decay in orbit
(green).}
\label{fig:RMC-RMD-DIO}
\end{figure}
Based on published branching ratios, we expect about 5000 RMC events
above 57~MeV from the aluminium target.
The resulting high energy photon spectra will be evaluated for their suitability
for normalisation in the Mu2e and COMET experiments.
We will also detect the spectrum of electrons from ordinary muon decay, which
are identified by requiring a time coincidence between the LYSO signal
and a signal from a scintillator placed in front of the LYSO.