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