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thesis/chapters/chap5_alcap_setup.tex
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@@ -2,10 +2,40 @@
\label{cha:the_alcap_run_2013}
\thispagestyle{empty}
The first run of the AlCap experiment was performed at the $\pi$E1 beam line
area, PSI (Figure~\ref{fig:psi_exp_hall_all}) from November 26 to December 23,
area, PSI from November 26 to December 23,
2013. The goal of the run was to measure protons rate and spectrum following
muon capture on aluminium.
\section{Experimental set up}
\label{sec:experimental_set_up}
The low energy muons from the $\pi$E1 beam line were stopped in thin aluminium
and silicon targets, and charged particles emitted were measured by two pairs
of silicon detectors inside of a vacuum vessel
(\cref{fig:alcap_setup_detailed}). A stopped muon event is defined by
a group of upstream detectors and a muon veto plastic scintillator.
The number of stopped muons is monitored by a germanium detector placed outside
of the vacuum chamber. In addition, several plastic scintillators were used to
provide veto signals for the silicon and germanium detectors. Two liquid
scintillators for neutron measurements were also tested in this run.
\begin{figure}[btp]
\centering
\includegraphics[width=0.55\textwidth]{figs/alcap_setup_detailed}
\caption{AlCap detectors: two silicon packages inside the vacuum vessel,
muon beam detectors including plastic scintillators and a wire chamber,
germanium detector and veto plastic scintillators.}
\label{fig:alcap_setup_detailed}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Muon beam and vacuum chamber}
Muons in the $\pi$E1 beam line are decay products of pions created
as a \SI{590}{\mega\electronvolt} proton beam hits a thick carbon target
(E-target in \cref{fig:psi_exp_hall_all}). The beam line was designed to
deliver muons with momenta ranging from
\SIrange{10}{500}{\mega\electronvolt\per\cc} and
momentum spread from \SIrange{0.26}{8.0}{\percent}. These parameters can be
selected by changing various magnets and slits shown in
\cref{fig:psi_piE1_elements}~\cite{Foroughli.1997}.
\begin{figure}[p]
\centering
\includegraphics[height=0.85\textheight]{figs/psi_exp_hall_all}
@@ -15,37 +45,7 @@ muon capture on aluminium.
\label{fig:psi_exp_hall_all}
\end{figure}
\section{Experimental set up}
\label{sec:experimental_set_up}
The low energy muons from the $\pi$E1 beam line were stopped in thin aluminium
and silicon targets, and charged particles emitted were measured by two pairs
of silicon detectors inside of a vacuum vessel
(Figure~\ref{fig:alcap_setup_detailed}). A stopped muon event is defined by
a group of upstream detectors and a muon veto plastic scintillator.
The number of stopped muons is monitored by a germanium detector placed outside
of the vacuum chamber. In addition, several plastic scintillators were used to
provide veto signals for the silicon and germanium detectors. Two liquid
scintillators for neutron measurements were also tested in this run.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.65\textwidth]{figs/alcap_setup_detailed}
\caption{AlCap detectors: two silicon packages inside the vacuum vessel,
muon beam detectors including plastic scintillators and a wire chamber,
germanium detector and veto plastic scintillators.}
\label{fig:alcap_setup_detailed}
\end{figure}
\subsection{Muon beam and vacuum chamber}
Muons in the $\pi$E1 beam line are decay products of pions created
as a 590~\mega\electronvolt\ proton beam hit a thick carbon target
(E-target in Figure~\ref{fig:psi_exp_hall_all}). The beam line was designed to
deliver muons with momenta ranging from 10 to 500~\mega\electronvolt\per\cc\
and
momentum spread from 0.26 to 8.0\%. These parameters can be selected by
changing various magnets and slits shown in
Figure~\ref{fig:psi_piE1_elements}~\cite{Foroughli.1997}.
\begin{figure}[htb]
\begin{figure}[btp]
\centering
\includegraphics[width=0.7\textwidth]{figs/psi_piE1_elements}
\caption{The $\pi$E1 beam line}
@@ -54,16 +54,17 @@ Figure~\ref{fig:psi_piE1_elements}~\cite{Foroughli.1997}.
One of the main requirements of the AlCap experiment was a low energy muon beam
with narrow momentum bite in order to achieve a high fraction of stopping muons
in the very thin targets. In this Run 2013, muons from 28 to
45~\mega\electronvolt\per\cc\ and momentum spread of 1\% and 3\%were used.
in the very thin targets. In this Run 2013, muons from
\SIrange{28}{45}{\mega\electronvolt\per\cc} and momentum spread of 1\% and
3\%were used.
For part of the experiment the target was replaced with one of the silicon
detector packages allowed an accurate momentum and range calibration
%(via range-energy relations)
of the beam at the target. Figure~\ref{fig:Rates} shows the measured muon rates
of the beam at the target. \Cref{fig:Rates} shows the measured muon rates
as a function of momentum for two different momentum bites.
Figure~\ref{fig:Beam} shows an example of the resulting energy spectra.
\begin{figure}[htbp]
\Cref{fig:Beam} shows an example of the resulting energy spectra.
\begin{figure}[btp]
\centering
\includegraphics[width=0.6\textwidth]{figs/Rates.png}
\caption{Measured muon rate (kHz) at low momenta. Momentum bite of 3 and 1 \%
@@ -71,18 +72,18 @@ Figure~\ref{fig:Beam} shows an example of the resulting energy spectra.
\label{fig:Rates}
\end{figure}
\begin{figure}[htbp]
\begin{figure}[btp]
\centering
\includegraphics[width=0.9\textwidth]{figs/beam.pdf}
\caption{Energy deposition at 36.4 MeV/c incident muon beam in an
1500-\micron-active
target. The peak at low energy is due to beam electrons, the
peaks at higher energies are due to muons. Momentum bite of 1 and 3\% FWHM
on left and right hand side, respectively.} \label{fig:Beam}
\caption{Energy deposition at \SI{36.4}{/c} incident muon beam in an
\SI{1500}{\micro\meter}-thick active target. The peak at low energy is due
to beam electrons, the peaks at higher energies are due to muons. Momentum
bite of 1 and 3\% FWHM on left and right hand side, respectively.}
\label{fig:Beam}
\end{figure}
The targets and charged particle detectors are installed inside the vacuum
chamber as shown in Figure~\ref{fig:alcap_setup_detailed}. The muon beam enters
chamber as shown in \cref{fig:alcap_setup_detailed}. The muon beam enters
from the right of the image and hits the target, which is placed at the
centre of the vacuum chamber and orientated at 45 degrees to the beam axis.
The side walls and bottom flange of the vessel provide several
@@ -91,7 +92,7 @@ scintillator detectors inside the chamber.
In addition, the chamber is equipped with several lead collimators
%so that muons that are not captured in the target would quickly decay.
to quickly capture muons that do not stop in the actual target.
%\begin{figure}[htbp]
%\begin{figure}[btp]
%\centering
%\includegraphics[width=0.55\textwidth]{figs/SetupOverview.jpg}
%\caption{Vacuum chamber in beam line}
@@ -102,22 +103,25 @@ to quickly capture muons that do not stop in the actual target.
%a silicon detector in the low vacuum region of $10^{-3}$ mbar.
%An interlock mechanism was installed to prevent the bias of the
%silicon detectors from being applied before the safe vacuum level.
For a safe operation of the silicon detector, a vacuum of $<10^{-4}$\,mbar was
necessary. With the help of the vacuum group of PSI, we could consistently
reach $10^{-4}$\,mbar within 45 minutes after closure of the chamber's top
flange.
For a safe operation of the silicon detector, a vacuum of \SI{e-4}{\milli\bar}
was necessary. With the help of the vacuum group of PSI, we could consistently
reach the required vacuum level within 45 minutes after closure of the
chamber's top flange.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Silicon detectors}
The main detectors for proton measurement in the Run 2013 were four large area
silicon detectors. The silicon detectors were grouped into two detector
packages located symmetrically at 90 degrees of the nominal muon beam path, SiL
and SiR in Figure~\ref{fig:alcap_setup_detailed}. Each arm consists of: one
$\Delta$E counter, a 65-\micro\meter-thick silicon detector, divided into
4 quadrants; one E counter made from 1500-\micron-thick silicon; and one
plastic scintillator to identify electrons or high energy protons that pass
through the silicon. The area of each of these silicon detectors and the
scintillators is $50\times50 \textrm{mm}^2$.
and SiR in \cref{fig:alcap_setup_detailed}. Each arm consists of: one
$\Delta$E counter, a \SI{65}{\micro\meter}-thick silicon detector, divided into
4 quadrants; one E counter made from \SI{1500}{\micro\meter}-thick silicon; and
one plastic scintillator to identify electrons or high energy protons that
pass through the silicon. The area of each of these silicon detectors and the
scintillators is $50\times50 \textrm{mm}^2$. There is a dead layer of
\SI{0.5}{\micro\meter} on each side of the silicon detectors according to the
manufacturer Micron Semiconductor
\footnote{\url{http://www.micronsemiconductor.co.uk/}}.
The detectors were named according to their positions relative to the muon
view: the SiL package contains the thin
@@ -129,11 +133,11 @@ SiR1-4.
Bias for the four silicon detectors was supplied by an ORTEC 710 NIM module,
which has a vacuum interlock input to prevent biasing before the safe vacuum
level has been reached. Typical voltage to fully depleted the detectors were
-300~\volt\ and -10~\volt\ for the thick and thin silicon detectors
\SI{-300}{\volt} and \SI{-10}{\volt} for the thick and thin silicon detectors
respectively. The leakage currents at the operating voltages are less than
1.5~\micro\ampere\ for the thick detectors, and about 0.05~\micro\ampere\
for the thin ones (see Figure~\ref{fig:si_leakage}).
\begin{figure}[htb]
\SI{1.5}{\micro\ampere} for the thick detectors, and about
\SI{0.05}{\micro\ampere} for the thin ones (see \cref{fig:si_leakage}).
\begin{figure}[btp]
\centering
\includegraphics[width=0.85\textwidth]{figs/si_leakage}
\caption{Leakage currents of the silicon detectors under bias.}
@@ -146,8 +150,8 @@ output
pulse height on an oscilloscope. One would expect that the maximum pulse height
increases as the bias is raised until the voltage of fully depleted. The effect
can also be seen on the pulse height spectrum as in
Figure~\ref{fig:sir2_bias_alpha}.
\begin{figure}[htb]
\cref{fig:sir2_bias_alpha}.
\begin{figure}[btp]
\centering
\includegraphics[width=0.75\textwidth]{figs/sir2_bias_alpha}
\caption{$^{241}\textrm{Am}$ spectra in cases of fully depleted (top), and
@@ -195,12 +199,12 @@ Figure~\ref{fig:sir2_bias_alpha}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Upstream counters}
\label{sub:upstream_counters}
The upstream detector consists of three counters: a 500~$\mu$m thick
scintillator muon trigger counter ($\mu$SC); a muon anti-coincidence counter
($\mu$SCA) surrounding the trigger counter with a hole
of 35 \milli\meter\ in diameter to define the beam radius; and a multi-wire
proportional chamber ($\mu$PC) that uses 24 X wires and 24 Y wires at
2~\milli\meter~intervals.
The upstream detector consists of three counters: a \SI{500}{\micro\meter}-thick
scintillator muon trigger counter (\Pmu{}SC); a muon anti-coincidence counter
(\Pmu{}SCA) surrounding the trigger counter with a hole
of 35 \si{\milli\meter}\ in diameter to define the beam radius; and a multi-wire
proportional chamber (\Pmu{}PC) that uses 24 X wires and 24 Y wires at
2~\si{\milli\meter}~intervals.
The upstream detectors provide signal of an incoming muon as coincident hits on
the muon trigger and the wire chamber in anti-coincident with the muon
@@ -214,7 +218,7 @@ ready to be used in our run without any modification.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Germanium detector}
%\begin{figure}[htbp]
%\begin{figure}[btp]
%\centering
%\includegraphics[width=0.9\textwidth]{figs/neutron.png}
%\caption{Setup of two
@@ -225,9 +229,9 @@ We used a germanium detector to normalise the number of stopped muons by
measuring characteristics muon X-rays from the target material. The primary
X-rays of interest are the 346.828~keV line for aluminium targets, and the
400.177 line for silicon targets. The energies and intensities of the X-rays
listed in Table~\ref{tab:xray_ref} follow measurement results from
listed in \cref{tab:xray_ref} follow measurement results from
Measday and colleagues~\cite{MeasdayStocki.etal.2007}.
\begin{table}[htb]
\begin{table}[btp]
\begin{center}
\begin{tabular}{c l l l l }
\toprule
@@ -250,11 +254,11 @@ The germanium detector is
a GMX20P4-70-RB-B-PL, n-type, coaxial high purity germanium detector produced
by ORTEC. The detector was optimised for low energy gamma and X-rays
measurement with an ultra-thin entrance window of 0.5-mm-thick beryllium and
a 0.3-\micron-thick ion implanted contact (Figure~\ref{fig:ge_det_dimensions}).
a 0.3-\si{\micro\meter}-thick ion implanted contact (\cref{fig:ge_det_dimensions}).
This detector is equipped with a transistor reset preamplifier which,
according to the producer, enables it to work in an ultra-high rate environment
up to $10^6$ counts\per\second~ at 1~\mega\electronvolt.
\begin{figure}[htb]
up to $10^6$ counts\si{\per\second} at \SI{1}{\mega\electronvolt}.
\begin{figure}[btp]
\centering
\includegraphics[width=0.9\textwidth]{figs/ge_det_dimensions}
\caption{Dimensions of the germanium detector}
@@ -288,12 +292,12 @@ carried out.
\section{Front-end electronics and data acquisition system}
The front-end electronics of the AlCap experiment was simple since we employed
a trigger-less read out system with waveform digitisers and flash ADCs
(FADCs). As shown in Figure~\ref{fig:alcapdaq_scheme}, all plastic
(FADCs). As shown in \cref{fig:alcapdaq_scheme}, all plastic
scintillators signals were amplified by PMTs, then fed into the digitisers. The
signals from silicon and germanium detectors were preamplified, and
subsequently shaped by spectroscopy amplifiers and timing filter amplifiers
(TFAs) to provide energy and timing information.
\begin{figure}[htbp]
\begin{figure}[btp]
\centering
\includegraphics[width=0.99\textwidth]{figs/alcapdaq_scheme}
\caption{Schematic diagram of the electronics and DAQ used in the Run 2013}
@@ -304,21 +308,21 @@ The germanium detector has its own transistor reset preamplifier
installed very close to the germanium crystal. Two ORTEC Model 142
preamplifiers were used for the thick silicon detectors. The timing outputs of
the preamplifiers were fed into three ORTEC Model 579 TFAs.
We used an ORTEC Model 673 to shape the germanium signal with 6~\micro\second
We used an ORTEC Model 673 to shape the germanium signal with 6~\si{\micro\second}
shaping time.
A more modern-style electronics was used for thin silicon detectors where the
preamplifier, shaping and timing amplifiers were implemented on one compact
package, namely a Mesytec MSI-8 box. This box has 8 channels, each channel
consists of one preamplifier board and one shaper-and-timing filter board which
can be fine-tuned independently. The shaping time was set to 1~\micro\second\
can be fine-tuned independently. The shaping time was set to 1~\si{\micro\second}\
for all channels.
The detector system produced signals that differs significantly in time scale,
ranging from very fast (about 40~\nano\second\ from scintillators) to very slow
(several \micro\second\ from shaping outputs of semiconductor detectors). This
lead to the use of several sampling frequencies from 17~\mega\hertz\ to
250~\mega\hertz, and three types of digitisers were employed:
ranging from very fast (about 40~\si{\nano\second}\ from scintillators) to very slow
(several \si{\micro\second}\ from shaping outputs of semiconductor detectors). This
lead to the use of several sampling frequencies from 17~\si{\mega\hertz}\ to
250~\si{\mega\hertz}, and three types of digitisers were employed:
\begin{itemize}
\item custom-built 12-bit 170-MHz FADCs which was designed for the
MuCap experiment. Each FADC board has dimensions the same as those of
@@ -328,10 +332,10 @@ lead to the use of several sampling frequencies from 17~\mega\hertz\ to
Ethernet-level protocol. The protocol only allows detecting
incomplete data transfers but no retransmitting is possible due to the
limited size of the module's output buffer. The FADCs accept clock signal
at the frequency of 50~\mega\hertz\ then multiply that internally up to
170~\mega\hertz. Each channel on one board can run at different sampling
at the frequency of 50~\si{\mega\hertz}\ then multiply that internally up to
170~\si{\mega\hertz}. Each channel on one board can run at different sampling
frequency not dependent on other channels. The FADC has 8 single-ended
LEMO inputs with 1~\volt pp dynamic range.
LEMO inputs with 1~\si{\volt} pp dynamic range.
\item a 14-bit 100-MS/s CAEN VME FADC waveform digitiser model V1724. The
module houses 8 channels with 2.25~Vpp dynamic range on single-ended MCX
coaxial inputs. The digitiser features an optical link for transmission of
@@ -347,7 +351,7 @@ lead to the use of several sampling frequencies from 17~\mega\hertz\ to
proprietary binary drivers and libraries.
\end{itemize}
All digitisers were driven by external clocks which were derived from the same
500-\mega\hertz\ master clock, a high precision RF signal generator Model SG382
500-\si{\mega\hertz}\ master clock, a high precision RF signal generator Model SG382
of Stanford Research System.
The silicon detectors were read out by FADC boards feature network-based data
@@ -355,14 +359,14 @@ readout interface. To maximize the data throughput, each of the four FADC
boards was read out through separate network adapter.
The CAEN digitisers were used to read out
the germanium detector (timing and energy, slow signals) or scintillator
detectors (fast signals). For redundancy, all beam monitors ($\mu$SC, $\mu$SCA
and $\mu$PC) were also read out by a CAEN time-to-digital converter (TDC)
detectors (fast signals). For redundancy, all beam monitors (\Pmu{}SC, \Pmu{}SCA
and \Pmu{}PC) were also read out by a CAEN time-to-digital converter (TDC)
model V767 which was kindly provided by the MuSun experiment.
The Data Acquisition System (DAQ) of the AlCap experiment, so-called AlCapDAQ,
provided the readout of front-end electronics, event assembling, data logging,
hardware monitoring and control, and the run database of the experiment
(Figure~\ref{fig:alcapdaq_pcs}). It was based on MIDAS framework~\footnote{
(\cref{fig:alcapdaq_pcs}). It was based on MIDAS framework~\footnote{
MIDAS is a general purpose DAQ software system developed at PSI and TRIUMF:\\
\url{http://midas.triumf.ca}} and consisted of two circuits, {\em i})
a detector circuit for synchronous data readout from the front-end electronics
@@ -375,7 +379,7 @@ running Linux operating system and connected into a private subnetwork.
%\hl{TODO: storage and shift monitor}
\begin{figure}[htb]
\begin{figure}[btp]
\centering
\includegraphics[width=0.95\textwidth]{figs/alcapdaq_pcs}
\caption{AlCapDAQ in the Run 2013. The {\ttfamily fe6} front-end is
@@ -397,10 +401,10 @@ correlation between detectors would be established in the analysis stage.
At the beginning of each block, the time counter in each digitiser is reset to
ensure time alignment across all modules. The period of 110~ms was chosen to be:
{\em i} long enough compares to the time scale of several \micro\second\ of the
{\em i} long enough compares to the time scale of several \si{\micro\second}\ of the
physics of interest, {\em ii} short enough so that there is no timer rollover
on any digitiser (a FADC runs at its maximum speed of 170~\mega\hertz\ could
handle up to about 1.5 \second\ with its 28-bit time counter).
on any digitiser (a FADC runs at its maximum speed of \SI{170}{\mega\hertz} could
handle up to about \SI{1.5}{\second} with its 28-bit time counter).
To ease the task of handling data, the data collecting period was divided into
short runs, each run stopped when the logger had recorded 2 GB of data.
@@ -431,14 +435,14 @@ different targets were carried out for silicon targets:
As the emitted protons deposit a significant amount of energy in the target
material, thin targets and thus excellent momentum resolution of the low energy
muon beam are critical. Aluminium targets of 50-\micro\meter\ and
100~\micron\ thick were used. Although a beam with low momentum spread of
muon beam are critical. Aluminium targets of 50-\si{\micro\meter}\ and
100~\si{\micro\meter}\ thick were used. Although a beam with low momentum spread of
1\% is preferable, it was used for only a small portion of the run due to the
low beam rate (see Figure~\ref{fig:Rates}). The beam momentum for each target
low beam rate (see \cref{fig:Rates}). The beam momentum for each target
was chosen to maximise the number of stopped muons. The collected data sets are
shown in Table~\ref{tb:stat}.
shown in \cref{tb:stat}.
\begin{table}[htb!]
\begin{table}[btp!]
\begin{center}
\vspace{0.15cm}
\begin{tabular}{l c c c}
@@ -446,16 +450,16 @@ shown in Table~\ref{tb:stat}.
\textbf{Target} &\textbf{Momentum} & \textbf{Run time} & \textbf{Number}\\
\textbf{and thickness}&\textbf{scaling factor} & \textbf{(h)} &\textbf{of muons}\\
\midrule
Si 1500 \micro\meter& 1.32& 3.07& $2.78\times 10^7$\\
Si 1500 \si{\micro\meter}& 1.32& 3.07& $2.78\times 10^7$\\
& 1.30& 12.04& $2.89 \times 10^8$\\
& 1.10& 9.36& $1.37 \times 10^8$ \\
\midrule
Si 62 \micro\meter & 1.06& 10.29& $1.72 \times 10^8$\\
Si 62 \si{\micro\meter} & 1.06& 10.29& $1.72 \times 10^8$\\
\midrule
Al 100 \micro\meter& 1.09& 14.37&$2.94 \times 10^8$\\
Al 100 \si{\micro\meter}& 1.09& 14.37&$2.94 \times 10^8$\\
& 1.07& 2.56& $4.99 \times 10^7$\\
\midrule
Al 50 \micro\meter m & 1.07& 51.94& $8.81 \times 10^8$\\
Al 50 \si{\micro\meter} m & 1.07& 51.94& $8.81 \times 10^8$\\
\bottomrule
\end{tabular}
\end{center}
@@ -473,11 +477,11 @@ Since the AlCapDAQ is a trigger-less system, it stored all waveforms of the
hits occured in 100-ms-long blocks without considering their physics
significance The analysis code therefore must be able to extract parameters of
the waveforms, then organises the pulses into physics events correlated to
stopped muons (Figure~\ref{fig:muon_event}). In addition, the analyser is
stopped muons (\cref{fig:muon_event}). In addition, the analyser is
intended to be usable as a real-time component of a MIDAS DAQ, where simple
analysis could be done online for monitoring and diagnostic during the run.
\begin{figure}[htb]
\begin{figure}[btp]
\centering
\includegraphics[width=0.9\textwidth]{figs/muon_event.pdf}
\caption{Concept of the AlCap analysis code: pulses from individual detector
@@ -520,7 +524,7 @@ algorithm that takes the pulse parameters from the peak of the waveform. In
parallel, a pulse finding and template fitting code is being developed because
it would provide more accurate pulse information. The first iteration of this
code has been completed and is being tested.
\begin{figure}[htb]
\begin{figure}[btp]
\centering
\includegraphics[width=0.85\textwidth]{figs/analysis_scheme}
\caption{Concept of the analysis framework in \rootana{}}
@@ -545,7 +549,7 @@ detectors. These particle hits are still stored in the time-ordered tree
corresponds to the 110 ms block length from the AlCapDAQ. By iterating through
the tree to find stopped muons and taking any hits within a certain window
around this muon from every detector, a stopped-muon-centred tree shown in
Figure~\ref{fig:muon_event} can be produced. This will make it much easier to
\cref{fig:muon_event} can be produced. This will make it much easier to
look for coincidences and apply cuts, thereby bringing the end
goal of particle numbers and energy distributions.
@@ -558,8 +562,8 @@ The online analyser was developed and proved to be very useful during the run.
A few basic modules were used to produce plots for diagnostic purposes
including: persistency view of waveforms, pulse height
spectra, timing correlations with respect to the upstream counters. The
modules and their purposes are listed in Table~\ref{tab:online_modules}.
\begin{table}[htb]
modules and their purposes are listed in \cref{tab:online_modules}.
\begin{table}[btp]
\begin{center}
\begin{tabular}{l p{6cm}}
\toprule
@@ -604,7 +608,7 @@ groups such as upstream counters, silicon arms. It could also periodically
update the plots to reflect real-time status of the detector system.
%Screen
%shots of the {\ttfamily online-display} with several plots are shown in
%Figure~\ref{fig:online_display}.
%\cref{fig:online_display}.
%\hl{Screen shots}
\subsection{Offline analyser}
@@ -612,15 +616,15 @@ update the plots to reflect real-time status of the detector system.
Some offline analysis modules has been developed during the beam time and could
provide quick feedback in confirming and guiding the decisions at the time. For
example, the X-ray spectrum analysis was done to confirm that we could observe
the muon capture process (Figure~\ref{fig:muX}), and to help in choosing optimal
the muon capture process (\cref{fig:muX}), and to help in choosing optimal
momenta which maximised the number of stopped muons.
\begin{figure}[htbp]
\begin{figure}[btp]
\centering
\includegraphics[width=0.7\textwidth]{figs/muX.png}
\caption{Germanium
detector spectra in the range of 300 - 450 keV with different setups: no
target, 62-\micron-thick silicon target, and 100-\micron-thick aluminium
target. The ($2p-1s$) lines from
target, 62-\si{\micro\meter}-thick silicon target, and
100-\si{\micro\meter}-thick aluminium target. The ($2p-1s$) lines from
aluminium (346.828 keV) and silicon (400.177 keV) are clearly visible,
the double peaks at 431 and 438 keV are from the lead shield, the peak at
351~keV is a background gamma ray from $^{211}$Bi.}

111
thesis/chapters/chap6_analysis.tex
View File

@@ -4,7 +4,7 @@
\section{Analysis modules}
\label{sec:analysis_modules}
A full analysis has not been completed yet, but initial analysis
based on the existing modules (Table~\ref{tab:offline_modules}) is possible
based on the existing modules (\cref{tab:offline_modules}) is possible
thanks to the modularity of the analysis framework.
\begin{table}[htb]
@@ -30,16 +30,16 @@ thanks to the modularity of the analysis framework.
\end{table}
The MakeAnalysedPulses module takes a raw waveform, calculates the pedestal
from a predefined number of first samples, subtracts this pedestal, takes
from a predefined number of first samples, subtracts this pedestal taking
pulse polarity into account, then calls another module to extract pulse
parameters. At the moment, the simplest module, so-called MaxBinAPGenerator,
for pulse information calculation is in use. The module looks for the
sample that
has the maximal deviation from the baseline, takes the deviation as pulse
amplitude and the time stamp of the sample as pulse time. The procedure is
illustrated on Figure~\ref{fig:tap_maxbin_algo}. This module could not detect
illustrated on \cref{fig:tap_maxbin_algo}. This module could not detect
pile up or double pulses in one \tpulseisland{} in
Figure~\ref{fig:tap_maxbin_bad}.
\cref{fig:tap_maxbin_bad}.
\begin{figure}[htb]
\centering
\includegraphics[width=0.85\textwidth]{figs/tap_maxbin_algo}
@@ -82,7 +82,7 @@ the beam rate was generally less than \SI{8}{\kilo\hertz}.
%candidate: a prompt hit on the target in $\pm 200$ \si{\nano\second}\ around the
%time of the $\mu$Sc pulse. The number comes from the observation of the
%time correlation between hits on the target and the $\mu$Sc
%(Figure~\ref{fig:tme_sir_prompt_rational}).
%(\cref{fig:tme_sir_prompt_rational}).
%\begin{figure}[htb]
%\centering
%\includegraphics[width=0.85\textwidth]{figs/tme_sir_prompt_rational}
@@ -97,7 +97,7 @@ rate, time correlation to hits on $\mu$Sc, \ldots on each channel during the
data collecting period. Runs with significant difference from the nominal
values were further checked for possible causes, and would be discarded if such
discrepancy was too large or unaccounted for. Examples of such trend plots are
shown in Figure~\ref{fig:lldq}.
shown in \cref{fig:lldq}.
\begin{figure}[htb]
\centering
\includegraphics[width=0.47\textwidth]{figs/lldq_noise}
@@ -131,15 +131,10 @@ During data taking period, electrons in the beam were were also used for energy
calibration of thick silicon detectors where energy deposition is large enough.
The muons at different momenta provided another mean of calibration in the beam
tuning period.
%Typical pulse height spectra of the silicon detectors are shown
%in Figure~\ref{fig:si_eg_spectra}.
According to Micron Semiconductor
\footnote{\url{http://www.micronsemiconductor.co.uk/}}, the
manufacturer of the silicon detectors, the nominal thickness of the dead layer on
each side is 0.5~\si{\micro\meter}. The alpha particles from the source would deposit
about 66~keV in this layer, and the peak would appear at 5418~keV
(Figure~\ref{fig:toyMC_alpha}).
The alpha particles from the source would deposit
about 66~keV in the \SI{0.5}{\micro\meter}-thick dead layer, and the peak would
appear at 5418~keV (\cref{fig:toyMC_alpha}).
\begin{figure}[htb]
\centering
\includegraphics[width=0.6\textwidth]{figs/toyMC_alpha}
@@ -149,7 +144,7 @@ about 66~keV in this layer, and the peak would appear at 5418~keV
\end{figure}
The calibration coefficients for the silicon channels are listed in
Table~\ref{tab:cal_coeff}.
\cref{tab:cal_coeff}.
\begin{table}[htb]
\begin{center}
\begin{tabular}{l c r}
@@ -183,7 +178,7 @@ source\footnote{Energies and intensities of gamma rays are taken from the
X-ray and Gamma-ray Decay Data Standards for Detector Calibration and Other
Applications, which is published by IAEA at \\
\url{https://www-nds.iaea.org/xgamma_standards/}}, the
recorded pulse height spectrum is shown in Figure~\ref{fig:ge_eu152_spec}. The
recorded pulse height spectrum is shown in \cref{fig:ge_eu152_spec}. The
source was placed at the target position so that the absolute efficiencies can
be calibrated. The relation between pulse height in ADC count and energy is
found to be:
@@ -197,7 +192,7 @@ worse at 3.1~\si{\kilo\electronvolt}~for the annihilation photons at
The absolute efficiencies for the $(2p-1s)$ lines of aluminium
(346.828~\si{\kilo\electronvolt}) and silicon (400.177~\si{\kilo\electronvolt}) are
presented in Table~\ref{tab:xray_eff}. In the process of efficiency calibration,
presented in \cref{tab:xray_eff}. In the process of efficiency calibration,
corrections for true coincidence summing and self-absorption were not applied.
The true coincidence summing probability is estimated to be very
small, about \sn{5.4}{-6}, thanks to the far geometry of the calibration. The
@@ -263,7 +258,7 @@ polyethylene is less than \sn{4}{-4} for a 100~\si{\kilo\electronvolt}\ photon.
%detector was placed perpendicular to the nominal beam path, after an oval
%collimator. The beam momentum scaling factor was scanned from 1.10 to 1.60,
%muon momenta and energies in the measured points are listed in
%Table~\ref{tab:mu_scales}.
%\cref{tab:mu_scales}.
%\begin{table}[htbp]
%\begin{center}
%\begin{tabular}{c c c c}
@@ -301,7 +296,7 @@ polyethylene is less than \sn{4}{-4} for a 100~\si{\kilo\electronvolt}\ photon.
\label{sec:charged_particles_from_muon_capture_on_silicon_thick_silicon}
This analysis was done on a subset of the active target runs 2119 -- 2140
because of the problem of wrong clock frequency found in the data quality
checking shown in Figure~\ref{fig:lldq}. The data set contains \sn{6.43}{7}
checking shown in \cref{fig:lldq}. The data set contains \sn{6.43}{7}
muon events.
%64293720
@@ -316,7 +311,7 @@ Because of the active target, a stopped muon would cause two coincident hits on
the muon counter and the target. The energy of the muon hit on the active
target is also well-defined as a narrow momentum spread beam was used. The
correlation between the energy and timing of all the hits on the active target
is shown in Figure~\ref{fig:sir2f_Et_corr}. The most intense spot at zero time
is shown in \cref{fig:sir2f_Et_corr}. The most intense spot at zero time
and about 5 MeV energy corresponds to stopped muons in the thick target. The
band below 1 MeV is due to electrons, either in the beam or from muon decay in
orbits, or emitted during the cascading of muon to the muonic 1S state. The
@@ -341,7 +336,7 @@ particles from the stopped muons:
It can be seen that there is a faint stripe of muons in the time larger than
1200~ns region, they are scattered muons by other materials without hitting the
muon counter. The electrons in the beam caused the constant band below 1 MeV and
$t > 5000$ ns (see Figure~\ref{fig:sir2_1us_slices}).
$t > 5000$ ns (see \cref{fig:sir2_1us_slices}).
\begin{figure}[htb]
\centering
\includegraphics[width=0.85\textwidth]{figs/sir2_sir2f_amp_1us_slices}
@@ -401,8 +396,8 @@ hits:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Number of charged particles with energy above 2~MeV}
\label{sub:number_of_charged_particles_with_energy_from_8_10_mev}
As shown in Figure~\ref{fig:sir2_1us_slices} and illustrated by MC simulation
in Figure~\ref{fig:sir2_mc_pdfs}, there are several components in
As shown in \cref{fig:sir2_1us_slices} and illustrated by MC simulation
in \cref{fig:sir2_mc_pdfs}, there are several components in
the energy spectrum recorded by the active target:
\begin{enumerate}
\item charged particles from nuclear muon capture, this is the signal we are
@@ -484,7 +479,7 @@ The number of nuclear captures can be inferred from the number of recorded
muonic X-rays. The reference values of the parameters needed for the
calculation taken from Suzuki et al.~\cite{SuzukiMeasday.etal.1987} and Measday
et al.~\cite{MeasdayStocki.etal.2007} are
listed in Table~\ref{tab:mucap_pars}.
listed in \cref{tab:mucap_pars}.
\begin{table}[htb]
\begin{center}
\begin{tabular}{l l l}
@@ -505,7 +500,7 @@ listed in Table~\ref{tab:mucap_pars}.
\end{table}
The muonic X-ray spectrum emitted from the active target is shown in
Figure~\ref{fig:sir2_xray}. The $(2p-1s)$ line is seen at
\cref{fig:sir2_xray}. The $(2p-1s)$ line is seen at
399.5~\si{\kilo\electronvolt}, 0.7~\si{\kilo\electronvolt}\ off from the
reference value of 400.177~\si{\kilo\electronvolt}. This discrepancy is within our
detector's resolution, and the calculated efficiency is
@@ -552,7 +547,7 @@ corrected for several effects:
pulse time, and (b) the reset pulses of the transistor reset preamplifier.
The effects of the two dead time could be calculated by examining the
interval between two consecutive pulses on the germanium detector in
Figure~\ref{fig:sir2_ge_deadtime}.
\cref{fig:sir2_ge_deadtime}.
\begin{figure}[htb]
\centering
\includegraphics[width=0.85\textwidth]{figs/sir2_ges_self_tdiff}
@@ -592,7 +587,7 @@ corrected for several effects:
\end{itemize}
The number of X-rays after applying all above corrections is 3293.5. The X-ray
intensity in Table~\ref{tab:mucap_pars} was normalised to the number of stopped
intensity in \cref{tab:mucap_pars} was normalised to the number of stopped
muons, so the number of stopped muons is:
\begin{align}
@@ -602,9 +597,9 @@ muons, so the number of stopped muons is:
&= 9.03\times10^6 \nonumber
\end{align}
where $\epsilon_{(2p-1s)}$ is the calibrated absolute efficiency of the
detector for the 400.177~keV line in Table~\ref{tab:xray_eff}, and
detector for the 400.177~keV line in \cref{tab:xray_eff}, and
$I_{(2p-1s)}$ is the probability of emitting this X-ray per stopped muon
(80.3\% from Table~\ref{tab:mucap_pars}).
(80.3\% from \cref{tab:mucap_pars}).
Taking the statistical uncertainty of the peak area, and systematic
uncertainties from parameters of muon capture, the number of stopped muons
@@ -621,7 +616,7 @@ The number of nuclear captured muons is:
\label{eqn:sir2_Ncapture}
\end{equation}
where the $f_{\textrm{cap.Si}}$ is the probability of nuclear capture per
stopped muon from Table~\ref{tab:mucap_pars}.
stopped muon from \cref{tab:mucap_pars}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Emission rate of charged particles}
\label{sub:emission_rate_of_charged_particles}
@@ -633,7 +628,7 @@ nuclear muon capture in~\eqref{eqn:sir2_Ncapture}:
= \frac{149.9\times10^4}{7.25\times10^6} = 0.252
\end{equation}
Uncertainties of this rate calculation are listed in
Table~\ref{tab:sir2_uncertainties}, including:
\cref{tab:sir2_uncertainties}, including:
\begin{itemize}
\item uncertainties from number of charged particles, both statistical and
systematic (from spectrum shape and fitting) ones are absorbed in the
@@ -690,7 +685,7 @@ So, the emission rate is:
%\label{fig:sobottka_spec}
%\end{figure}
%The spectrum measured by Sobottka and Wills~\cite{SobottkaWills.1968} is
%reproduced in Figure~\ref{fig:sobottka_spec}, the spectral integral in the
%reproduced in \cref{fig:sobottka_spec}, the spectral integral in the
%energy region from 8 to 10~\si{\mega\electronvolt}\ is $2086.8 \pm 45.7$.
%The authors obtained the spectrum in a 4~\si{\micro\second}\ gate period which began
%1~\si{\micro\second}\ after a muon stopped, which would take 26.59\% of the emitted
@@ -769,11 +764,11 @@ within a coincidence window of $\pm 0.5$~\si{\micro\second}\ around the thick
silicon hit, the two hits are considered to belong to one particle with
$\Delta$E being the energy of the thin hit, and total E being the sum energy of
the two hits. Particle identification is done using correlation between
$\Delta$E and E. Figure~\ref{fig:si16p_dedx_nocut} shows clearly visible banding
$\Delta$E and E. \cref{fig:si16p_dedx_nocut} shows clearly visible banding
structure. No cut on energy deposit or timing with respect to muon hit are
applied yet.
With the aid from MC study (Figure~\ref{fig:pid_sim}), the banding on the
With the aid from MC study (\cref{fig:pid_sim}), the banding on the
$\Delta$E-E plots can be identified as follows:
\begin{itemize}
\item the densest spot at the lower left conner belonged to electron hits;
@@ -804,13 +799,13 @@ $\Delta$E-E plots can be identified as follows:
\end{figure}
It is observed that the banding is more clearly visible in a log-log scale
plots like in Figure~\ref{fig:si16p_dedx_cut_explain}, this suggests
plots like in \cref{fig:si16p_dedx_cut_explain}, this suggests
a geometrical cut on the logarithmic scale would be able to discriminate
protons from other particles. The protons and deuterons bands are nearly
parallel to the $\ln(\Delta \textrm{E [keV]}) + \ln(\textrm{E [keV]})$ line,
but have a slightly altered slope because $\ln(\textrm{E})$ is always greater
than $\ln(\Delta\textrm{E})$. The two parallel lines on
Figure~\ref{fig:si16p_dedx_cut_explain} suggest a check of
\cref{fig:si16p_dedx_cut_explain} suggest a check of
$\ln(\textrm{E}) + 0.85\times\ln(\Delta \textrm{E})$ could tell
protons from other particles.
@@ -829,11 +824,11 @@ $\ln(\textrm{E}) < 9$, which corresponds to $\textrm{E} < 8$~MeV.
The cut of $\ln(\textrm{E}) < 9$ is applied first, then
$\ln(\textrm{E})+ 0.85\times\ln(\Delta \textrm{E}) $ is plotted as
Figure~\ref{fig:si16p_loge+logde}. The protons make a clear peak in the region
\cref{fig:si16p_loge+logde}. The protons make a clear peak in the region
between 14 and 14.8, the next peak at 15 corresponds to deuteron.
Imposing the
$14<\ln(\textrm{E})+ 0.85\times\ln(\Delta \textrm{E})<14.8$ cut,
the remaining proton band is shown on Figure~\ref{fig:si16p_proton_after_ecut}.
the remaining proton band is shown on \cref{fig:si16p_proton_after_ecut}.
\begin{figure}[htb]
\centering
@@ -854,7 +849,7 @@ the remaining proton band is shown on Figure~\ref{fig:si16p_proton_after_ecut}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Number of muon captures}
\label{sub:number_stopped_muons}
The X-ray spectrum from this silicon target on Figure~\ref{fig:si16_xray} is
The X-ray spectrum from this silicon target on \cref{fig:si16_xray} is
significantly noisier than the previous data set of SiR2, suffers from both
lower statistics and a more relaxed muon definition. The peak of $(2p-1s)$
X-ray at 400.177~keV can still be recognised but on a very high background. The
@@ -881,7 +876,7 @@ reducing the background level under the 400.177 keV peak by about one third.
Using the same procedure on the region from 396 to 402 keV (without
self-absorption correction since this is a thin target), the number of
X-rays recorded and the number of captures are shown in
Table~\ref{tab:si16p_ncapture_cal}.
\cref{tab:si16p_ncapture_cal}.
\begin{table}[htb]
\begin{center}
\begin{tabular}{l l c c c}
@@ -920,8 +915,8 @@ Table~\ref{tab:si16p_ncapture_cal}.
To check the origin of the protons recorded, lifetime measurements were made by
cutting on time difference between a hit on one thick silicon and the muon
hit. Applying the time cut in 0.5~\si{\micro\second}\ time steps on the proton
events in Figure~\ref{fig:si16p_proton_after_ecut}, the number of surviving
protons on each arm are plotted on Figure~\ref{fig:si16p_proton_lifetime}. The
events in \cref{fig:si16p_proton_after_ecut}, the number of surviving
protons on each arm are plotted on \cref{fig:si16p_proton_lifetime}. The
curves show decay constants of $762.9 \pm 13.7$~\si{\nano\second}\ and $754.6 \pm
11.9$,
which are consistent with the each other, and with mean life time of muons in
@@ -939,7 +934,7 @@ The fits are consistent with lifetime of muons in silicon in from after 500~ns,
before that, the time constants are shorter ($655.9\pm 9.9$ and $731.1\pm8.9$)
indicates the contamination from muon captured on material with higher $Z$.
Therefore a timing cut from 500~ns is used to select good silicon events, the
remaining protons are shown in Figure~\ref{fig:si16p_proton_ecut_500nstcut}.
remaining protons are shown in \cref{fig:si16p_proton_ecut_500nstcut}.
The spectra have a low energy cut off at 2.5~MeV because protons with energy
lower than that could not pass through the thin silicon to make the cuts as the
range of 2.5~MeV protons in silicon is about 68~\si{\micro\meter}.
@@ -954,7 +949,7 @@ range of 2.5~MeV protons in silicon is about 68~\si{\micro\meter}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Proton emission rate from the silicon target}
\label{sub:proton_emission_rate_from_the_silicon_target}
The number of protons in Figure~\ref{fig:si16p_proton_ecut_500nstcut} is
The number of protons in \cref{fig:si16p_proton_ecut_500nstcut} is
counted from 500~ns after the muon event, where the survival rate is
$e^{-500/758} = 0.517$.
@@ -974,7 +969,7 @@ The emission rate per muon capture is:
&= \dfrac{2.625 \times 10^5}{6.256\times10^6} \nonumber\\
&= 4.20\times10^{-2}\nonumber
\end{align}
The proton spectra on the Figure~\ref{fig:si16p_proton_ecut_500nstcut} and the
The proton spectra on the \cref{fig:si16p_proton_ecut_500nstcut} and the
emission rate are only effective ones, since the energy of protons are modified
by energy loss in the target, and low energy protons could not escape the
target. Therefore further corrections are needed for both rate and spectrum of
@@ -989,11 +984,11 @@ The uncertainty of the emission rate could come from several sources:
background under the X-ray peak (5.5\%) and the efficiency calibration
\item number of protons: efficiency of the cuts in energy, impacts of the
timing resolution on timing cut. The energy cuts' contribution should be
small since it can be seen from Figure~\ref{fig:si16p_loge+logde}, the peak
small since it can be seen from \cref{fig:si16p_loge+logde}, the peak
of protons is strong and well separated from others. The uncertainty in
timing contribution is significant because all the timing done in this
analysis was on the peak of the slow signals. As it is clear from the
Figure~\ref{fig:tme_sir_prompt_rational}, the timing resolution of the
\cref{fig:tme_sir_prompt_rational}, the timing resolution of the
silicon detector could not be better than 100~ns. Putting $\pm100$~ns into
the timing cut could change the survival rate of proton by about
$1-e^{-100/758} \simeq 13\%$. Also, the low statistics contributes a few
@@ -1024,7 +1019,7 @@ By using only the lower limit on
$\ln(\textrm{E}) + 0.85\times\ln(\Delta \textrm{E})$, the heavy charged
particles can be selected. These particles also show a lifetime that is
consistent with that of muons in silicon
(Figure~\ref{fig:si16p_allparticle_lifetime}).
(\cref{fig:si16p_allparticle_lifetime}).
\begin{figure}[htb]
\centering
\includegraphics[width=0.85\textwidth]{figs/si16p_allparticle_lifetime}
@@ -1041,7 +1036,7 @@ The ratio between the number of protons and other particles at 500~ns is $(1927
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Rate and spectrum correction}
%\label{sub:proton_spectrum_deconvolution}
%The proton spectra on the Figure~\ref{fig:si16p_proton_ecut_500nstcut} and the
%The proton spectra on the \cref{fig:si16p_proton_ecut_500nstcut} and the
%emission rate are only effective ones, since the energy of protons are modified
%by energy loss in the target, and low energy protons could not escape the
%target. Therefore corrections are needed for both rate and spectrum of protons.
@@ -1054,7 +1049,7 @@ The ratio between the number of protons and other particles at 500~ns is $(1927
%The initial spatial distribution of protons is inferred from the muon beam
%momentum using Monte Carlo simulation, and available measured data in momentum
%scanning runs. The response function for this thin silicon target is shown in
%Figure~\ref{fig:si16p_toyMC}.
%\cref{fig:si16p_toyMC}.
%\begin{figure}[htb]
%\centering
%\includegraphics[width=0.85\textwidth]{figs/si16p_toyMC}
@@ -1069,7 +1064,7 @@ The ratio between the number of protons and other particles at 500~ns is $(1927
%The Bayesian method is chosen because it tends to be fast, typical number of
%iterations is from 4--8.
%Figure~\ref{fig:si16p_unfold_train} presented results of two tests unfolding with
%\cref{fig:si16p_unfold_train} presented results of two tests unfolding with
%two distributions of initial energy, a Gaussian distribution and
%a parameterized function in~\eqref{eqn:EH_pdf}. The numbers of protons obtained
%from the tests show agreement with the generated numbers.
@@ -1084,8 +1079,8 @@ The ratio between the number of protons and other particles at 500~ns is $(1927
%\end{figure}
%Finally, the unfolding is applied on the spectra in
%Figure~\ref{si16p_proton_spec}, the results are shown in
%Figure~\ref{si16p_unfold_meas}.
%\cref{si16p_proton_spec}, the results are shown in
%\cref{si16p_unfold_meas}.
%\begin{figure}[htb]
%\centering
%\includegraphics[width=0.85\textwidth]{figs/si16p_unfold_meas}
@@ -1127,7 +1122,7 @@ passive silicon runs were applied.
\subsection{The number of stopped muons}
\label{sub:the_number_of_stopped_muons}
The X-ray spectrum on the germanium detector is shown on
Figure~\ref{fig:al100_ge_spec}.
\cref{fig:al100_ge_spec}.
\begin{figure}[htb]
\centering
\includegraphics[width=0.85\textwidth]{figs/al100_ge_spec}
@@ -1153,7 +1148,7 @@ target are:
\label{sub:particle_identification}
Using the same charged particle selection
procedure and the cuts on $\ln(\textrm{E})$ and $\ln(\Delta\textrm{E})$, the
proton energy spectrum is shown in Figure~\ref{fig:al100_proton_spec}.
proton energy spectrum is shown in \cref{fig:al100_proton_spec}.
\begin{figure}[htb]
\centering
\includegraphics[width=1\textwidth]{figs/al100_selection}
@@ -1163,13 +1158,13 @@ proton energy spectrum is shown in Figure~\ref{fig:al100_proton_spec}.
\end{figure}
The lifetime of these protons are shown in
Figure~\ref{fig:al100_proton_lifetime}, the fitted decay constant on the right
\cref{fig:al100_proton_lifetime}, the fitted decay constant on the right
arm is consistent with the reference value of $864 \pm 2$~\si{\nano\second}~\cite{}.
But the left arm gives $918 \pm 16.1$~\si{\nano\second}, significantly larger than
the reference value.
%The longer lifetime suggested some contributions from
%other lighter materials, one possible source is from muons captured on the back
%side of the collimator (Figure~\ref{fig:alcap_setup_detailed}).
%side of the collimator (\cref{fig:alcap_setup_detailed}).
%For this reason, the emission rate calculated from the left arm will be taken as upper
%limit only.
\begin{figure}[htb]
@@ -1185,7 +1180,7 @@ and the decay constant on the SiL1-1 alone was nearly about 1000~\si{\micro\seco
The reason for this behaviour is not known yet. For this emission rate
calculation, this channel is discarded and the rate on the left arm is scaled
with a factor of 4/3. The proton spectrum from the aluminium target is plotted
on Figure~\ref{fig:al100_proton_spec_wosil11}.
on \cref{fig:al100_proton_spec_wosil11}.
\begin{figure}[htb]
\centering