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14
thesis/chapters/chap4_alcap_phys.tex
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@@ -736,7 +736,7 @@ smaller in cases of Al and Cu, and about 10 times higher in case of AgBr
\begin{center} \begin{center}
\begin{tabular}{l l c} \begin{tabular}{l l c}
\toprule \toprule
\textbf{Nucleus} & \textbf{Exp.$\times 10^3$} & \textbf{MEC cal.$\times \textbf{Nucleus} & \textbf{Experiment$\times 10^3$} & \textbf{Calculation$\times
10^3$}\\ 10^3$}\\
\midrule \midrule
Al & $1.38 \pm 0.09$ & 0.3\\ Al & $1.38 \pm 0.09$ & 0.3\\
@@ -748,9 +748,10 @@ smaller in cases of Al and Cu, and about 10 times higher in case of AgBr
\bottomrule \bottomrule
\end{tabular} \end{tabular}
\end{center} \end{center}
\caption{Probability of proton emission with $E_p \ge 40$ \caption{Probability of proton emission with $E_p \ge \SI{40}{\MeV}$
\si{\MeV}~as calculated by Lifshitz and calculated by Lifshitz and
Singer~\cite{LifshitzSinger.1988} in comparison with available data.} Singer~\cite{LifshitzSinger.1988} with the two-nucleon capture hypothesis
in comparison with available data.}
\label{tab:lifshitzsinger_cal_proton_rate_1988} \label{tab:lifshitzsinger_cal_proton_rate_1988}
\end{table} \end{table}
% subsection theoretical_models (end) % subsection theoretical_models (end)
@@ -825,7 +826,7 @@ protons should be affordable.
The proton absorber solves the problem of hit rate, but it degrades the The proton absorber solves the problem of hit rate, but it degrades the
reconstructed momentum resolution. Therefore its thickness and geometry should reconstructed momentum resolution. Therefore its thickness and geometry should
be carefully optimised. The limited information available makes it difficult to be carefully optimised. The limited information available makes it difficult to
arrive at a conclusive detector design. The proton emission rate could be 0.97\% arrive at a conclusive detector design. The proton emission rate could be 4\%
as calculated by Lifshitz and Singer~\cite{LifshitzSinger.1980}; or 7\% as as calculated by Lifshitz and Singer~\cite{LifshitzSinger.1980}; or 7\% as
estimated from the $(\mu^-,\nu pn)$ activation data and the ratio in estimated from the $(\mu^-,\nu pn)$ activation data and the ratio in
\eqref{eqn:wyttenbach_ratio}; or as high as 15-20\% from silicon and neon. \eqref{eqn:wyttenbach_ratio}; or as high as 15-20\% from silicon and neon.
@@ -836,7 +837,8 @@ are adopted follow the silicon data from Sobottka and Will
~\cite{SobottkaWills.1968}. The spectrum shape is fitted with an empirical ~\cite{SobottkaWills.1968}. The spectrum shape is fitted with an empirical
function given by: function given by:
\begin{equation} \begin{equation}
p(T) = A\left(1-\frac{T_{th}}{T}\right)^\alpha \exp{-\frac{T}{T_0})}, p(T) = A\left(1-\frac{T_{th}}{T}\right)^\alpha
\exp{\left(-\frac{T}{T_0}\right)},
\label{eqn:EH_pdf} \label{eqn:EH_pdf}
\end{equation} \end{equation}
where $T$ is the kinetic energy of the proton in \si{\MeV}, and the fitted where $T$ is the kinetic energy of the proton in \si{\MeV}, and the fitted

76
thesis/chapters/chap6_analysis.tex
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@@ -475,21 +475,22 @@ The yields of protons from \SIrange{4}{8}{\MeV} are:
\end{align} \end{align}
The number of emitted protons is taken as average of the two yields: The number of emitted protons is taken as average of the two yields:
\begin{equation} \begin{equation}
N_{\textrm{p unfold}} = (169.3 \pm 2.9) \times 10^3 N_{\textrm{p unfold}} = (169.3 \pm 1.9) \times 10^3
\end{equation} \end{equation}
\subsection{Number of nuclear captures} \subsection{Number of nuclear captures}
\label{sub:number_of_nuclear_captures} \label{sub:number_of_nuclear_captures}
\begin{figure}[htb] %\begin{figure}[!htb]
\centering %\centering
\includegraphics[width=0.85\textwidth]{figs/al100_ge_spec} %\includegraphics[width=0.85\textwidth]{figs/al100_ge_spec}
\caption{X-ray spectrum from the aluminium target, the characteristic %\caption{X-ray spectrum from the aluminium target, the characteristic
$(2p-1s)$ line shows up at 346.67~keV} %$(2p-1s)$ line shows up at 346.67~keV}
\label{fig:al100_ge_spec} %\label{fig:al100_ge_spec}
\end{figure} %\end{figure}
The X-ray spectrum on the germanium detector is shown on %The X-ray spectrum on the germanium detector is shown on
\cref{fig:al100_ge_spec}. Fitting the double peaks on top of a first-order %\cref{fig:al100_ge_spec}.
Fitting the double peaks on top of a first-order
polynomial gives the X-ray peak area of $5903.5 \pm 109.2$. With the same polynomial gives the X-ray peak area of $5903.5 \pm 109.2$. With the same
procedure as in the case of the active target, the number stopped muons and procedure as in the case of the active target, the number stopped muons and
the number of nuclear captures are: the number of nuclear captures are:
@@ -508,7 +509,15 @@ The proton emission rate in the range from \SIrange{4}{8}{\MeV} is therefore:
\end{equation} \end{equation}
The total proton emission rate can be estimated by assuming a spectrum shape The total proton emission rate can be estimated by assuming a spectrum shape
with the same parameterisation as in \eqref{eqn:EH_pdf}. The fit parameters with the same parameterisation as in \eqref{eqn:EH_pdf}. The
\eqref{eqn:EH_pdf} function has a power rising edge, and a exponential decay
falling edge. The falling edge has only one decay component and is suitable to
describe the proton spectrum with the equilibrium emission only assumption.
The pre-equilibrium emission contribution should be small for low-$Z$ material,
for aluminium the contribution of this component is 2.2\% according to
Lifshitz and Singer~\cite{LifshitzSinger.1980}.
The fitted results
are shown in \cref{fig:al100_parameterisation} and \cref{tab:al100_fit_pars}. are shown in \cref{fig:al100_parameterisation} and \cref{tab:al100_fit_pars}.
The average spectrum is obtained by taking the average of the two unfolded The average spectrum is obtained by taking the average of the two unfolded
spectra from the left and right arms. The fitted parameters are compatible spectra from the left and right arms. The fitted parameters are compatible
@@ -534,7 +543,7 @@ protons. The total proton emission rate is therefore estimated to be $3.5\times
$A \times 10^{-5}$ & 2.0 \pm 0.7 & 1.3 \pm 0.1 & 1.5 \pm 0.3\\ $A \times 10^{-5}$ & 2.0 \pm 0.7 & 1.3 \pm 0.1 & 1.5 \pm 0.3\\
$T_{th}$ (\si{\keV}) & 1301 \pm 490 & 1966 \pm 68 & 1573 \pm 132\\ $T_{th}$ (\si{\keV}) & 1301 \pm 490 & 1966 \pm 68 & 1573 \pm 132\\
$\alpha$ & 3.2 \pm 0.7 & 1.2 \pm 0.1 & 2.0 \pm 1.2\\ $\alpha$ & 3.2 \pm 0.7 & 1.2 \pm 0.1 & 2.0 \pm 1.2\\
$T_{th}$ (\si{\keV}) & 2469 \pm 203 & 2641 \pm 106 & 2601 \pm 186\\ $T_{0}$ (\si{\keV}) & 2469 \pm 203 & 2641 \pm 106 & 2601 \pm 186\\
\bottomrule \bottomrule
\end{tabular} \end{tabular}
\end{center} \end{center}
@@ -597,7 +606,7 @@ presented in \cref{tab:al100_uncertainties_all}.
\textbf{Item}& \textbf{Value} \\ \textbf{Item}& \textbf{Value} \\
\midrule \midrule
Number of muons & 3.2\% \\ Number of muons & 3.2\% \\
Statistical from measured spectra & 1.6\% \\ Statistical from measured spectra & 1.1\% \\
Systematic from unfolding & 5.0\% \\ Systematic from unfolding & 5.0\% \\
Systematic from PID & \textless0.5\% \\ Systematic from PID & \textless0.5\% \\
\midrule \midrule
@@ -638,7 +647,7 @@ validated:
\subsection{Proton emission rates and spectrum} \subsection{Proton emission rates and spectrum}
\label{sub:proton_emission_rates_and_spectrum} \label{sub:proton_emission_rates_and_spectrum}
The proton emission spectrum in \cref{sub:proton_emission_rate} peaks around The proton emission spectrum in \cref{sub:proton_emission_rate} peaks around
\SI{4}{\MeV} which is comparable to the Coulomb barrier for proton of \SI{3.7}{\MeV} which is a little below the Coulomb barrier for proton of
\SI{3.9}{\MeV} calculated using \eqref{eqn:classical_coulomb_barrier}. The \SI{3.9}{\MeV} calculated using \eqref{eqn:classical_coulomb_barrier}. The
spectrum has a decay constant of \SI{2.6}{\MeV} in higher energy region, spectrum has a decay constant of \SI{2.6}{\MeV} in higher energy region,
makes the emission probability drop more quickly than silicon charged makes the emission probability drop more quickly than silicon charged
@@ -661,29 +670,48 @@ all energy is:
R_{p \textrm{ total}} = (3.5 \pm 0.2)\%. R_{p \textrm{ total}} = (3.5 \pm 0.2)\%.
\label{eqn:meas_total_rate} \label{eqn:meas_total_rate}
\end{equation} \end{equation}
No direct comparison of this result to existing experimental or
theoretical work is available. Indirectly, it is compatible with the figures \subsubsection{Comparison to theoretical and other experimental results}
calculated by Lifshitz and \label{ssub:comparison_to_theoretical_and_other_experimental_results}
There is no existing experimental or theoretical work that could be directly
compared with the obtained proton emission rate. Indirectly, it is compatible
with the figures calculated by Lifshitz and
Singer~\cite{LifshitzSinger.1978, LifshitzSinger.1980} listed in Singer~\cite{LifshitzSinger.1978, LifshitzSinger.1980} listed in
\cref{tab:lifshitzsinger_cal_proton_rate}. It is significantly larger than \cref{tab:lifshitzsinger_cal_proton_rate}. It is significantly larger than
the rate of 0.97\% for the $(\mu,\nu p)$ channel, and does not the rate of 0.97\% for the $(\mu,\nu p)$ channel, and does not
exceed the inclusion rate for all channels $\Sigma(\mu,\nu p(xn))$ at 4\%, exceed the inclusion rate for all channels $\Sigma(\mu,\nu p(xn))$ at 4\%,
leaving some room for other modes such as $(\mu,\nu d)$ or $(\mu,\nu p2n)$. leaving some room for other modes such as emission of deuterons or tritons.
Certainly, if the rate of deuterons can be extracted then the combined Certainly, when the full analysis is available, deuterons and tritons emission
emission rate of protons and deuterons could be compared directly with the rates could be extracted and the combined emission rate could be compared
inclusive rate. directly with the inclusive rate.
The result \eqref{eqn:meas_total_rate} is greater than the The result \eqref{eqn:meas_total_rate} is greater than the
probability of the reaction $(\mu,\nu pn)$ measured by Wyttenbach et probability of the reaction $(\mu,\nu pn)$ measured by Wyttenbach et
al.~\cite{WyttenbachBaertschi.etal.1978} at 2.8\%. It is expectable because al.~\cite{WyttenbachBaertschi.etal.1978} at 2.8\%. It is expectable because
the contribution from the $(\mu,\nu d)$ channel should be small since it the contribution from the $(\mu,\nu d)$ channel should be small since it
needs to form a deuteron from a proton and a neutron. needs to form a deuteron from a proton and a neutron.
The rate of 3.5\% was estimated with an assumption that all protons are
emitted in equilibrium. With the exponential constant of \SI{2.6}{\MeV}, the
proton yield in the range from \SIrange{40}{70}{\MeV} is negligibly small
($\sim\num{E-8}$). However, Krane and colleagues reported a significant yield
of 0.1\% in that region~\cite{KraneSharma.etal.1979}. The energetic proton
spectrum shape also has a different exponential constant of \SI{7.5}{\MeV}. One
explanation for these protons is that they are emitted by other mechanisms,
such as capture on two-nucleon cluster suggested by Singer~\cite{Singer.1961}
(see \cref{sub:theoretical_models} and
\cref{tab:lifshitzsinger_cal_proton_rate_1988}). Despite being sizeable, the
yield of high energy protons is still small (3\%) in compared with the result
in \eqref{eqn:meas_total_rate}.
%The $(\mu^-,\nu p):(\mu^-,\nu pn)$ ratio is then roughly 1:1, not 1:6 as in %The $(\mu^-,\nu p):(\mu^-,\nu pn)$ ratio is then roughly 1:1, not 1:6 as in
%\eqref{eqn:wyttenbach_ratio}. %\eqref{eqn:wyttenbach_ratio}.
Compared with emission rate from silicon, the result \subsubsection{Comparison to the silicon result}
\eqref{eqn:meas_total_rate} is indeed much smaller. It is even lower than \label{ssub:comparison_to_the_silicon_result}
the rate of the no-neutron reaction $(\mu,\nu p)$. This can be explained as The probability of proton emission per nuclear capture of 3.5\% is indeed much
smaller than that of silicon. It is even lower than the rate of the no-neutron
reaction $(\mu,\nu p)$. This can be explained as
the resulted nucleus from muon capture on silicon, $^{28}$Al, is an odd-odd the resulted nucleus from muon capture on silicon, $^{28}$Al, is an odd-odd
nucleus and less stable than that from aluminium, $^{27}$Mg. The proton nucleus and less stable than that from aluminium, $^{27}$Mg. The proton
separation energy for $^{28}$Al is \SI{9.6}{\MeV}, which is significantly separation energy for $^{28}$Al is \SI{9.6}{\MeV}, which is significantly

48
thesis/chapters/chap7_results.tex
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@@ -43,8 +43,10 @@ recorded (see \cref{fig:cdc_toy_mc_p_spec_500um}).
\begin{figure}[!htb] \begin{figure}[!htb]
\centering \centering
\includegraphics[width=0.75\textwidth]{figs/cdc_toy_mc_p_spec_500um} \includegraphics[width=0.75\textwidth]{figs/cdc_toy_mc_p_spec_500um}
\caption{Toy MC study of the CDC hit rate due to protons. The absorber \caption{Proton energy spectra at different stages from birth to the
thickness was set at \SI{0.5}{\mm} in this plot.} sensitive volume of the CDC. The baseline design of \SI{0.5}{\mm} thick
absorber and \SI{0.5}{\mm} thick inner wall was used to produce this
plot.}
\label{fig:cdc_toy_mc_p_spec_500um} \label{fig:cdc_toy_mc_p_spec_500um}
\end{figure} \end{figure}
@@ -55,34 +57,44 @@ layer due to these protons with
different absorber thickness are shown in \cref{tab:proton_cdc_hitrate}. different absorber thickness are shown in \cref{tab:proton_cdc_hitrate}.
\begin{table}[htb] \begin{table}[htb]
\begin{center} \begin{center}
\begin{tabular}{S S S S} \begin{tabular}{S S S S S}
\toprule \toprule
{\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}& {\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}&
{\textbf{Proton}}\\ {\textbf{Proton}} & {\textbf{Momentum}}\\
{\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}& {\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}&
{\textbf{hit rate}}\\ {\textbf{hit rate}} &{\textbf{spread $\Delta p$}}\\
{(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})}\\ {(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})}
& {(\si{\keV\per\cc)}}\\
\midrule \midrule
1 &0.5&1.5 & 2\\ 1 &0.5&1.5 & 2 & 195\\
0.5 &0.5&1.0 & 126\\ 0.5 &0.5&1.0 & 126 & 167\\
0 &0.5&0.5 & 1436\\ 0 &0.5&0.5 & 1436 & 133\\
0 &0.3&0.3 & 8281\\ 0 &0.3&0.3 & 8281 & {-}\\
0 &0.1&0.1 & 15011\\ 0 &0.1&0.1 & 15011& {-}\\
\bottomrule \bottomrule
\end{tabular} \end{tabular}
\end{center} \end{center}
\caption{CDC proton hit rates} \caption{CDC proton hit rates at different configuration of proton absorber
and inner wall. The momentum spreads for \SI{0.5}{\mm} thick inner wall are
taken from \cref{tab:comet_absorber_impact}.}
\label{tab:proton_cdc_hitrate} \label{tab:proton_cdc_hitrate}
\end{table} \end{table}
At the baseline design of \SI{0.5}{\mm}, the hit rate is only \SI{126}{\Hz}, At the baseline design of \SI{0.5}{\mm}, the hit rate is only \SI{126}{\Hz},
much smaller than the current estimation at \SI{34}{\kHz}. Even without the much smaller than the current estimation at \SI{34}{\kHz}. Even without the
absorber, proton hit rate remains low at \SI{1.4}{\kHz}. Therefore a proton absorber, proton hit rate remains low at \SI{1.4}{\kHz}.
absorber is not needed for the COMET Phase I's CDC. %Therefore a proton
%absorber is not needed for the COMET Phase I's CDC.
Without the proton absorber, the momentum spread of the signal electron If the proton absorber is not used, the momentum spread of the signal electron
reduces from \SI{167}{\keV} to \SI{131}{\keV}. If a lower momentum spread is reduces from \SI{167}{\keV} to \SI{131}{\keV}. In case a lower momentum spread
desired, it is possible to reduce the thickness of the inner wall. The last is desired, it is possible to reduce the thickness of the inner wall. The last
two rows of \cref{tab:proton_cdc_hitrate} show that even with thinner walls at two rows of \cref{tab:proton_cdc_hitrate} show that even with thinner walls at
\SI{0.3}{\mm} and \SI{0.1}{\mm} the hit rate by protons are still at \SI{0.3}{\mm} and \SI{0.1}{\mm} the hit rate by protons are still at
manageable levels. manageable levels. However, reducing the wall thickness would be governed by
other requirements such as mechanical structure and gas-tightness.
In summary, the toy MC study with the preliminary proton rate and spectrum
shows that a proton absorber is not needed. It confirms the known fact that the
estimation used in COMET Phase-I is conservative, and provides a solid
prediction of the hit rate caused by protons.

28
thesis/chapters/chap8_conclusions.tex
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@@ -1,6 +1,6 @@
\chapter{Conclusions} \chapter{Conclusions}
\label{cha:conclusions} \label{cha:conclusions}
AlCap is an experiment proposed at PSI to study charged particles, neutrons The AlCap is an experiment proposed at PSI to study charged particles, neutrons
and photons emitting after nuclear muon capture on aluminium. These and photons emitting after nuclear muon capture on aluminium. These
measurements are important for backgrounds and hit rates estimation of the new measurements are important for backgrounds and hit rates estimation of the new
generation of \mueconv experiments, COMET and Mu2e. In the first stage of the generation of \mueconv experiments, COMET and Mu2e. In the first stage of the
@@ -9,23 +9,33 @@ dominated by low energy protons following muon capture on an aluminium target,
which has never been measured. which has never been measured.
The first run of the AlCap which aims for proton measurement has been carried The first run of the AlCap which aims for proton measurement has been carried
out in 2013. Data analysis is in progress. An initial analysis on partial data out in 2013. Data analysis is in progress. Before finishing the complete AlCap
was done with the main results are: analysis, an initial analysis on partial data
was made. The main results are:
\begin{enumerate} \begin{enumerate}
\item Demonstration of the analysis chain from raw waveforms to physics \item demonstration of the analysis chain from trigger-less waveforms to
events; correlated physics events;
\item Validation of the experimental method including: number of nuclear \item validation of the experimental method including: number of nuclear
capture muons normalisation by muonic X-ray measurement, charged particle capture muons normalisation by muonic X-ray measurement, charged particle
identification by specific energy loss, and unfolding of the proton energy identification by specific energy loss, and unfolding of the proton energy
spectrum using the iterative Bayesian method; spectrum using the iterative Bayesian method;
\item Obtaining preliminary results on proton emission rate and spectrum: \item obtaining preliminary results on proton emission rate and spectrum:
the proton spectrum has a peak at \SI{4}{\MeV}, then reduces exponentially the proton spectrum has a peak at \SI{3.7}{\MeV}, then reduces exponentially
with a decay constant of \SI{2.6}{\MeV}. The partial emission rate in the with a decay constant of \SI{2.6}{\MeV}. The partial emission rate in the
energy range from \SIrange{4}{8}{\MeV} is $(1.7 \pm 0.1)\%$, and the total energy range from \SIrange{4}{8}{\MeV} is $(1.7 \pm 0.1)\%$, and the total
emission rate assuming the shape holds for the whole spectrum is emission rate assuming the shape holds for the whole spectrum is
$(3.5\pm0.2)$. $(3.5\pm0.2)$.
\end{enumerate} \end{enumerate}
The emission rate is consistent with the lower limit of 2.8\% set by
Wyttenbach et al.~\cite{WyttenbachBaertschi.etal.1978}. It is also compatible
with the theoretical calculation by Lifshitz and
Singer~\cite{LifshitzSinger.1980}. Compared with the emission rate from
silicon, our result is smaller.
The proton rate and spectrum have been used to optimise the planned proton The proton rate and spectrum have been used to optimise the planned proton
absorber for the drift chamber of the COMET Phase-I. The resulted proton hit absorber for the drift chamber of the COMET Phase-I. The resulted proton hit
rate with the baseline configuration is very small compared with the current rate with the baseline configuration is very small compared with the current
figure. It is safe to remove the proton absorber altogether. figure. It is safe to remove the proton absorber altogether. This would make
a strong impact to the drift chamber design. The AlCap experiment is going to
submit a beam time request for the 2015 run to collect more data and other
measurements for neutrons and gamma rays.

2
thesis/chapters/frontmatter.tex
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@@ -32,7 +32,7 @@ aluminium have been carried out in the 2013 run. The second run to study
neutrons and photons is planned in 2015. neutrons and photons is planned in 2015.
The preliminary results from the analysis of the 2013 run are presented in this The preliminary results from the analysis of the 2013 run are presented in this
thesis. The measured proton spectrum peaks at \SI{4}{\MeV} and decays thesis. The measured proton spectrum peaks at \SI{3.7}{\MeV} and decays
exponentially with the decay constant of \SI{2.6}{\MeV}. The emission exponentially with the decay constant of \SI{2.6}{\MeV}. The emission
rate of protons in the energy range from \SIrange{4}{8}{\MeV} is rate of protons in the energy range from \SIrange{4}{8}{\MeV} is
$(1.7\pm0.1)\%$. The total proton emission rate is estimated to be $(1.7\pm0.1)\%$. The total proton emission rate is estimated to be

2
thesis/mythesis.sty
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@@ -12,7 +12,7 @@ inner=1.25in, outer=1in, twoside]{geometry}
%$ Hyper-link .. %$ Hyper-link ..
\RequirePackage[% \RequirePackage[%
colorlinks=true,% color links instead of using boxes colorlinks=false,% color links instead of using boxes
linkcolor=red,% color for internal (intra-document) links linkcolor=red,% color for internal (intra-document) links
citecolor=green,% color for bibliographic links citecolor=green,% color for bibliographic links
urlcolor=blue,% color for URL links urlcolor=blue,% color for URL links