118 lines
5.7 KiB
TeX
118 lines
5.7 KiB
TeX
The X-ray analysis is used to determine the number of stopped muons in the
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AlCap target by counting the number of
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muonic X-rays produced. In addition to the X-rays, there are gamma rays
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that can be observed and are relevant to Mu2e/COMET as well as AlCap.
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The entrance beam scintillator
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counters can be used to count the muons
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as they enter the vacuum chamber, however
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collimation and accounting for
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those muons that pass through the thin target,
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the stopping efficiency in the target is significantly
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less than 100\%.
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The factor of interest for normalisation is the rate
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of muon nuclear capture inside the target. The branching ratio of
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capture is known for the targets of interest \cite{MeasdayAl} and is
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proportional to the number of muon stops.
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With the active silicon target
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we have a reliable method of detecting a stop, namely, an energy
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deposited in the silicon corresponding to the incoming muon beam energy, and
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a time coincidence between signals from the beam counters and the silicon
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detector. This is not the case with
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the passive silicon and aluminium targets, for which we use instead the muonic
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X-rays for normalisation.
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When a muon is captured by an atom, it gives off
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characteristic X-rays as it falls to the 1s state that can be counted
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to determine the stopping rate.
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For aluminium and silicon, the energies and intensities of the X-rays
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from the $2p\to1s$ transitions
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are well known and listed in Table~\ref{tab:xray_ref}.
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The stopping rate
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can then be inferred from the number of these X-rays measured,
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after accounting for
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geometric and photo-efficiencies. The rate from this method was cross-checked with that determined directly from stops in the active
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silicon target, and the numbers are within each other's uncertainties.
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A peak from the natural background ${}^{214}$Pb (351.9 keV) exists near
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the ${}^{27}$Al \atrn{2p}{1s} ($K_\alpha$) X-ray.
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To suppress this neighbouring peak and the
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background, we required an entering muon in time coincidence with the
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germanium pulse. However, we noticed that an unexpected
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$\gamma$ line prompt with muon nuclear capture on lead appears at a slightly
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lower energy than the ${}^{214}$Pb line (Figure \ref{fig:xrayanalysis:tl207}).
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This is consistent with an intermediate excited
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state of $^{207}$Tl, produced by muon capture on $^{208}$Pb.
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Though not spoiling our measurement, the classification of
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this peak is important so that it can be confirmed in the next run.
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\begin{figure}
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\centering
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\includegraphics[width=0.5\linewidth]{figs/tl207.png}
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\caption{To reduce the nearby pollution of the Al$_{K\alpha}$ by natural $^{214}$Pb,
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only germanium signals within 300 ns of an entering muon were examined. When
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the background peak persisted, we realised it was a prompt $\gamma$ from
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muon capture on lead going via an intermediate excited $^{207}$Tl$^*$ state. This was
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confirmed by the time structure of photons in that peak, which matches
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the muonic lead lifetime.}
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\label{fig:xrayanalysis:tl207}
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\end{figure}
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Though muonic X-rays are the primary method of normalisation in AlCap,
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there are others that can be used and since both Mu2e and COMET are interested
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in alternative normalisation schemes, it is important to examine the
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viability of other peaks as
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indicators of stopped muons. One is the $\gamma$ from the reaction
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$^{27}_{13}\mbox{Al}+\mu^-\to\nu_{\mu}+n+\gamma+^{26}_{12}\mbox{Mg}$, with an intensity of
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about 50\% per stopped
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muon and an energy of 1809 keV \cite{MeasdayAl}.
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What is appealing about this peak
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is that there are few nearby peaks to worry about, and the signal-to-noise
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ratio is
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favourable, see the data in Figure \ref{fig:xrayanalysis:mg26_1809}.
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The ratio of the number of observed
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counts in the 1809 keV gamma ray line relative to
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the $2p\to 1s$ muonic X-ray line is in good agreement with the value in the
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literature.
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\begin{figure}
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\centering
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\includegraphics[width=0.6\textwidth]{figs/mg26_1809keV}
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\caption{The $\gamma$ produced in
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$\mu^-+^{27}_{13}\mbox{Al}\to\nu_{\mu}+n+^{26}_{12}\mbox{Mg}^*$
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followed by $^{26}_{12}\mbox{Mg}^*\to ^{26}_{12}\mbox{Mg}+\gamma$,
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occurs at 1809 keV with an intensity of 0.51 per $\mu$-capture \cite{MeasdayAl}.
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Because this line occurs in such a clean region of the photon spectrum and is so intense,
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it could possibly be used for monitoring the number of stopped muons
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in Mu2e and COMET.}
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\label{fig:xrayanalysis:mg26_1809}
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\end{figure}
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A second gamma line at 844 keV results from the beta decay of
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the relatively long-lived (9.5 minutes) $^{27}$Mg isotope
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produced in the reaction
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$^{27}_{13}\mbox{Al}+\mu^-\to\nu_{\mu}+^{27}_{12}\mbox{Mg}$.
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Though counting this peak agreed within error with that expected from published
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branching ratios, the uncertainty is large due to poor statistics.
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By improving the statistics
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under this peak in the proposed run we will
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determine a more precise branching ratio, making it useful as a potential
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normalisation to the number of muon stops in Mu2e and COMET.
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The current data for this peak, as well as nearby peaks,
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is illustrated in figure \ref{fig:xrayanalysis:mg27_844kev}.
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\begin{figure}
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\centering
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\includegraphics[width=0.5\textwidth]{figs/mg27_844keV}
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\caption{A peak at 844 keV from the decay of $^{27}_{12}$Mg is
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correlated with the number of stopped muons in the target.
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Unfortunately the yield is low and additionally polluted
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by a nearby iron peak. With the statistics from our first run,
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we could not determine to a sufficient precision the number
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of these $\gamma$s we expect per captured muon, however we
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will be able to achieve this in the proposed next run when the statistics will be much improved.}
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\label {fig:xrayanalysis:mg27_844kev}
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\end{figure}
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