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updating the xray paper

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Nam Tran
2020-05-13 10:01:16 -05:00
parent 992edc2808
commit 5c1b39f38e
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3
r15a_xray/tex/abstract.tex
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@@ -1,3 +0,0 @@
\begin{abstract}
Abstract
\end{abstract}

16
r15a_xray/tex/analysis.tex
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@@ -130,7 +130,7 @@ and fractions of muons captured by element of interest are calculated and
listed in~\cref{tab:capture_frac}.
\begin{table}[tbp]
\centering
\caption{Nuclear capture probability calculated from mean lifetimes taken
\caption{Nuclear capture probabilities calculated from mean lifetimes taken
from measurements of Suzuki et.al.~\cite{SuzukiMeasday.etal.1987}}
\label{tab:capture_frac}
\begin{tabular}{cccc}
@@ -144,3 +144,17 @@ listed in~\cref{tab:capture_frac}.
\bottomrule
\end{tabular}
\end{table}
Number of stopped and captured muons in our targets are:
\begin{table}[tbp]
\centering
\caption{Number of muons stopped and captured}
\label{}
\begin{tabular}{ccc}
Target & Number of muons stopped & Number of muons captured \\
\midrule
\ce{^{nat}Al} & $(2.96002\pm 0.00017) \times 10^8$ & $(1.8041\pm 0.0015) \times 10^8$\\
\ce{^{nat}Ti} & $(2.17237\pm 0.00015) \times 10^8$ & $(1.8530\pm 0.0013) \times 10^8$\\
\ce{^{nat}W} & & \\
\end{tabular}
\end{table}

51
r15a_xray/tex/intro.tex
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@@ -1,11 +1,46 @@
\section{Introduction}
Why are we even doing this measurement?
\begin{itemize}
\item targets for mu-e conversion experiments
\item why did we measure \ce{W}, \ce{H_2O}, \ldots: background for Xrays of
interest in Mu2e
\item existing data? focused on nuclear charge radii, did not report muonic
X-ray yields. This is true for \ce{^{nat}Ti}~\cite{Wohlfahrt1981}
The next generation of charged leption flavor violation (CLFV) experiments
(COMET at J-PARC and Mu2e at Fermilab) are going to stop about \num{e18} muons
in their targets to search for new physics beyond the Standard Model. Knowing
accurately number of stopped muons in the targets is important as it is the
denominator for the branching ratio of the coherent muon decay to electron
without a neutrino process these experiments looking for. The proposed way to
measure the actual number of stopped muons is infering that from number of
charateristic muonic X-rays, and gamma rays emitted from excited nuclei after
muon capture.
\end{itemize}
Both COMET and Mu2e will use pulsed proton beam to produce pions which decay in
flight to muons. The primary beam line of Mu2e would deliver proton pulses
\SI{1.7}{\micro\second} apart, each pulse contains about \num{4E7} protons.
Electrons from decays of pions would hit the muon stopping target about
\SI{100}{\nano\second} earlier than muons do, and produce an intense
``beam~flash'' (about \SI{51}{\mega\hertz\per\square\centi\meter} of
bremsstrahlungs with average energy of
\SI{1.4}{\mega\electronvolt})~\cite{mu2etdr}. It is therefore challenging to
measure the X-rays and gamma rays mentioned above. The situation in COMET Phase-I
is similar~\cite{comettdr}.
There are two proposed target materials for COMET and Mu2e, namely aluminum and
titanium. Most prominent aluminum muonic X-rays at \SI{346.8}{\keV}
(\twoPoneS~transition) and \SI{412.8}{\keV} (\threePoneS~transition) were
measured precisely by Measday et
al.~\cite{Measday2007}. Observing these X-rays in a highly intense pulsed beam
experiment like COMET and Mu2e would be difficult as they might be buried by
the ``beam~flash'' described above. A gamma ray of \SI{1808.7}{\keV} from
\ce{^{26}Mg^*} would provide a better proxy to the number of stopped muons for
it has a lifetime of muon in aluminium, therefore can be measured out of the
``beam flash''. The emission rate of this gamma was measured at
\SI{10}{\percent} uncertainty in~\cite{Measday2007}.
Knowledge about muonic X-rays and gammas after muon capture on titanium is less
prehensive. Measurements of titanium were mostly done in context of either nuclear
charge radii~\cite{Wohlfahrt1981}, or neutrinoless double beta
decay~\cite{Zinatulina2019}, and did not report X-ray yeilds.
To have a more completed picture of the situation, AlCap has carried out
measurements of photons after muon capture on aluminum and titanium. The goals
are emission rates of charateristic muonic X-rays from titanium, and improvement
on the rate of the \SI{1808.7}{\keV} gamma from aluminum. In addion, we have
measured photons from other materials where muons would stop in the experiments
to learn about potential background around the gammas and X-rays of interest.

68
r15a_xray/tex/results.tex
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@@ -1,17 +1,9 @@
\section{Results and discussions}
\subsection{Titanium}
Number of stopped muons in the natural titanium target was:
Fitting the peak around \SI{932}{keV} in the photon spectrum gives energies of the $2p_{3/2}-1s$ and $2p_{1/2}-1s$ transitions as \SI{932.5 \pm 0.9}{\keV} and \SI{930.4 \pm 1.1}{\keV}, respectively. These values are consistent with previously reported values by Wohlfahrt et al.~\cite{Wohlfahrt1981} given the isotopic abundance of the natural titanium target used in this experiment. The
number of $(2p_{3/2}-1s)$ X-rays is:
\begin{equation}
N_{\mu} = (88296 \pm 9) \times 10^3 \,.
\label{eqn:Nmu_Ti_Tsc}
\end{equation}
Fitting the peak around \SI{931}{keV} in the photon spectrum gives the
center of gravity at \SI{931.6 \pm 0.7}{keV} (see~\cref{fig:ti_931keV_fit}),
consistent with previously reported value~\cite{Wohlfahrt1981}.
Number of $(2p-1s)$ X-rays in the \SI{931.6}{keV} peak is:
\begin{equation}
N_{931.6} = (20750 \pm 764) \,.
N_{2p_{3/2}-1s} = (11881 \pm 591) \,.
\end{equation}
\begin{figure}[tbp]
@@ -21,8 +13,52 @@ Number of $(2p-1s)$ X-rays in the \SI{931.6}{keV} peak is:
\label{fig:ti_931keV_fit}
\end{figure}
The emission rate of the $(2p-1s)$ muonic X-rays is calculated as:
\begin{equation}
R_{Ti} = \frac{N_{931.6}}{A_{931.6} \times N_{\mu} \times f_{capTi}} = 0.90
\pm 0.04 \,.
\end{equation}
Emission rates of K X-rays from titanium is listed in~\cref{tab:kXraysTi}.
\begin{table}[tbp]
\centering
\caption{Emission rates of K X-rays from titanium}
\label{tab:kXraysTi}
\begin{tabular}{ccc}
Transition & Energy [keV] & Rate [\%] \\
$2p-1s$ & 932.4 & \num{78.9\pm2.5}\\
$3p-1s$ & 1121.5 & \num{7.5\pm1.7}\\
$4p-1s$ & 1187.9 & \num{3.2\pm1.0}\\
$5p-1s$ & 1218.5 & \num{2.6\pm1.4}\\
$6p-1s$ & 1235.2 & \num{3.2\pm1.9}\\
\end{tabular}
\end{table}
\begin{figure}[tbp]
\centering
\includegraphics[width=0.8\textwidth]{figs/ti-kXrays.pdf}
\caption{Muonic X-rays in the Lyman series from titanium}
\label{fig:ti_kXrays}
\end{figure}
\subsection{Aluminum}
\label{subsec:result_al}
\begin{figure}[tbp]
\centering
\includegraphics[width=0.8\textwidth]{figs/al-kXrays.pdf}
\caption{Muonic X-rays in the Lyman series from aluminum}
\label{fig:al_kXrays}
\end{figure}
Emission rates of K X-rays from aluminum is listed in~\cref{tab:kXraysAl}.
\begin{table}[tbp]
\centering
\caption{Emission rates of K X-rays from aluminum}
\label{tab:kXraysAl}
\begin{tabular}{cccc}
Transition & Energy [keV] & Intensity (this experiment) [\%] & Intensity [\%]~\cite{Measday2007}\\
$2p-1s$ & 346.8 & \num{83.1\pm3.5} & \num{79.8\pm0.8}\\
$3p-1s$ & 412.8 & \num{7.71\pm0.29}& \num{7.6\pm1.5}\\
$4p-1s$ & 435.9 & \num{4.79\pm0.18}& \num{4.9\pm1.0}\\
$5p-1s$ & 446.6 & \num{3.81\pm0.14}& \num{3.9\pm1.0}\\
$6p-1s$ & 452.4 & \num{2.24\pm0.13}& \num{2.2\pm1.0}\\
\end{tabular}
\end{table}