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thesis2/chapters/chap6_analysis.tex
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@@ -3,7 +3,7 @@
\section{Analysis modules}
\label{sec:analysis_modules}
A full offline analysis has not been completed yet, but initial analysis
A full analysis has not been completed yet, but initial analysis
based on the existing modules (Table~\ref{tab:offline_modules}) is possible
thanks to the modularity of the analysis framework.
@@ -57,14 +57,14 @@ Figure~\ref{fig:tap_maxbin_bad}.
The TSimpleMuonEvent first picks a muon candidate, then loops through all
pulses on all detector channels, and picks all pulses occur in
a time window of $\pm 10$~\micro\second\ around each candidate to build a muon
event. A muon candidates is a hit on the upstream plastic scintillator with
an amplitude higher than a threshold which was chosen to reject minimum ionising
particles (MIPs). The
10~\micro\second\ is long enough compares to the mean life time of muons in the
target materials (0.758~\micro\second\ for silicon, and 0.864~\micro\second\ for
aluminium~\cite{SuzukiMeasday.etal.1987}) so practically all of emitted charged
particles would be recorded in this time window.
a time window of \SI{\pm 10}{\si{\micro\second}} around each candidate to build
a muon event. A muon candidates is a hit on the upstream plastic scintillator
with an amplitude higher than a threshold which was chosen to reject minimum
ionising particles (MIPs). The period of \SI{10}{\si{\micro\second}} is long
enough compares to the mean life time of muons in the target materials
(\SI{0.758}{\si{\micro\second}} for silicon, and \SI{0.864}{\si{\micro\second}}
for aluminium~\cite{SuzukiMeasday.etal.1987}) so practically all of emitted
charged particles would be recorded in this time window.
%\begin{figure}[htb]
%\centering
%\includegraphics[width=0.85\textwidth]{figs/tme_musc_threshold}
@@ -73,13 +73,13 @@ particles would be recorded in this time window.
%\end{figure}
A pile-up protection mechanism is employed to reject multiple muons events: if
there exists another muon hit in less than 15~\micro\second\ from the candidate
then both the candidate and the other muon are discarded. This pile-up
protection would cut out less than 11\% total number of events because the beam
rate was generally less than 8~\kilo\hertz.
there exists another muon hit in less than \SI{15}{\si{\micro\second}} from the
candidate then both the candidate and the other muon are discarded. This
pile-up protection would cut out less than 11\% total number of events because
the beam rate was generally less than \SI{8}{\kilo\hertz}.
%In runs with active silicon targets, another requirement is applied for the
%candidate: a prompt hit on the target in $\pm 200$ \nano\second\ around the
%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}).
@@ -120,11 +120,12 @@ shown in Figure~\ref{fig:lldq}.
The energy calibration for the silicon detectors were done routinely during the
run, mainly by an
$^{241}\textrm{Am}$ alpha source and a tail pulse generator. The source emits
79.5 $\alpha\per\second$ in a 2$\pi$~\steradian~solid angle. The most
prominent alpha particles have energies of 5.484~\mega\electronvolt\
(85.2\%) and 5.442~\mega\electronvolt\ (12.5\%). A tail pulse with amplitude of
66 \milli\volt~was used to simulate the response of the silicon detectors'
preamplifiers to a particle with 1\mega\electronvolt~energy deposition.
79.5 $\alpha$\si{\per\second} in a \SI{2\pi}{\steradian} solid angle. The most
prominent alpha particles have energies of \SI{5.484}{\si{\mega\electronvolt}}
(85.2\%) and \SI{5.442}{\si{\mega\electronvolt}} (12.5\%). A tail pulse with
amplitude of
\SI{66}{\milli\volt}~was used to simulate the response of the silicon detectors'
preamplifiers to a particle with \SI{1}{\si{\mega\electronvolt}} energy deposition.
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.
@@ -136,14 +137,14 @@ tuning period.
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~\micron. The alpha particles from the source would deposit
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}).
\begin{figure}[htb]
\centering
\includegraphics[width=0.6\textwidth]{figs/toyMC_alpha}
\caption{Energy loss of the alpha particles after a dead layer of
0.5~\micron.}
0.5~\si{\micro\meter}.}
\label{fig:toyMC_alpha}
\end{figure}
@@ -190,18 +191,18 @@ found to be:
\textrm{ E [keV]} = 0.1219 \times \textrm{ADC} + 1.1621
\end{equation}
The energy resolution (full width at half maximum) was better than
2.6~\kilo\electronvolt\ for all the $^{152}\textrm{Eu}$ peaks. It was a little
worse at 3.1~\kilo\electronvolt~for the annihilation photons at
511.0~\kilo\electronvolt.
2.6~\si{\kilo\electronvolt}\ for all the $^{152}\textrm{Eu}$ peaks. It was a little
worse at 3.1~\si{\kilo\electronvolt}~for the annihilation photons at
511.0~\si{\kilo\electronvolt}.
The absolute efficiencies for the $(2p-1s)$ lines of aluminium
(346.828~\kilo\electronvolt) and silicon (400.177~\kilo\electronvolt) are
(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,
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
absorption in the source cover made of 22~\milli\gram\per\centi\meter$^2$
polyethylene is less than \sn{4}{-4} for a 100~\kilo\electronvolt\ photon.
absorption in the source cover made of 22~\si{\milli\gram\per\si{\centi\meter}^2}
polyethylene is less than \sn{4}{-4} for a 100~\si{\kilo\electronvolt}\ photon.
\begin{table}[htb]
\begin{center}
@@ -224,8 +225,8 @@ polyethylene is less than \sn{4}{-4} for a 100~\kilo\electronvolt\ photon.
\caption{Energy spectrum of the $\rm^{152}\textrm{Eu}$ calibration source
recorded by the germanium detector. The most prominent peaks of
$^{152}\textrm{Eu}$ along with their energies are
annotated in red; the 1460.82 \kilo\electronvolt~line is background from
$^{40}\textrm{K}$; and the annihilation 511.0~\kilo\electronvolt~photons
annotated in red; the 1460.82 \si{\kilo\electronvolt}~line is background from
$^{40}\textrm{K}$; and the annihilation 511.0~\si{\kilo\electronvolt}~photons
come both from the source and the surrounding environment.}
\label{fig:ge_eu152_spec}
\end{figure}
@@ -505,8 +506,8 @@ listed in Table~\ref{tab:mucap_pars}.
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
399.5~\kilo\electronvolt, 0.7~\kilo\electronvolt\ off from the
reference value of 400.177~\kilo\electronvolt. This discrepancy is within our
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
$(4.549 \pm 0.108)\times 10^{-5}$ -- a 0.15\% increasing from that of the
400.177~keV line, so no attempt for recalibration or correction was made.
@@ -529,7 +530,7 @@ corrected for several effects:
\item Self-absorption effect: the X-rays emitted could be absorbed by the
target itself, the probability of self-absorption becomes larger in case of
thick sample and low energy photons.
For this silicon target of 1500~\micron\ thick and the photon energy of
For this silicon target of 1500~\si{\micro\meter}\ thick and the photon energy of
400~keV, and assuming a narrow muon stopping distribution at the centre of
the target, the self-absorption correction is estimated to be:
\begin{align}
@@ -556,8 +557,8 @@ corrected for several effects:
\centering
\includegraphics[width=0.85\textwidth]{figs/sir2_ges_self_tdiff}
\caption{Interval between to consecutive pulses on the germanium
detector. The peak at 57~\micro\second\ indicates the pulse length, and
the bump at about 2000~\micro\second\ shows the width of the reset
detector. The peak at 57~\si{\micro\second}\ indicates the pulse length, and
the bump at about 2000~\si{\micro\second}\ shows the width of the reset
pulses. The average count rate of this detector is extracted from the
decay constant of the time spectrum to be
$5.146 \times 10^{-7}\textrm{ ns}^{-1} = 514.6 \textrm{ s}^{-1}$}
@@ -690,13 +691,13 @@ So, the emission rate is:
%\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
%energy region from 8 to 10~\mega\electronvolt\ is $2086.8 \pm 45.7$.
%The authors obtained the spectrum in a 4~\micro\second\ gate period which began
%1~\micro\second\ after a muon stopped, which would take 26.59\% of the emitted
%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
%particles into account. The number of stopped muons was not explicitly stated,
%but can be inferred to be $55715/0.06 = 92858.3$.
%The partial rate of charged particle from 8 to 10~\mega\electronvolt\ is then
%The partial rate of charged particle from 8 to 10~\si{\mega\electronvolt}\ is then
%calculated to be:
%\begin{equation}
%R_{\textrm{8-10 MeV}}^{lit.} =
@@ -704,7 +705,7 @@ So, the emission rate is:
%= 1.28 \times 10^{-2}
%\end{equation}
%The authors did not mentioned how the uncertainties of their measurement was
%derived, but quoted the emission rate below 26~\mega\electronvolt\ to be $0.15
%derived, but quoted the emission rate below 26~\si{\mega\electronvolt}\ to be $0.15
%\pm 0.02$, which translates to a relative uncertainty of 0.133. The statistical
%uncertainty from the spectral integral and the number of stopped muons is:
%\begin{equation*}
@@ -712,14 +713,14 @@ So, the emission rate is:
%\end{equation*}
%Then their systematic uncertainty would be: $0.133 - 0.009 = 0.124$.
%For the partial spectrum from 8 to 10~\mega\electronvolt, the statistical
%For the partial spectrum from 8 to 10~\si{\mega\electronvolt}, the statistical
%contribution to the uncertainty is:
%\begin{equation*}
%\dfrac{1}{\sqrt{2086.8}} + \dfrac{1}{\sqrt{92858.3}} = 2.5 \times 10^{-2}
%\end{equation*}
%So, the combined uncertainty of this partial rate calculation is: $0.124
%+ 0.025 = 0.150$. The partial rate of charged particles from 8 to
%10~\mega\electronvolt per muon capture is:
%10~\si{\mega\electronvolt} per muon capture is:
%\begin{equation}
%R_{\textrm{8-10 MeV}}^{lit.} = (1.28 \pm 0.19) \times 10^{-2}
%\end{equation}
@@ -729,8 +730,8 @@ So, the emission rate is:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Charged particles following muon capture on a thin silicon target}
\label{sec:charged_particles_following_muon_capture_on_a_thin_silicon_target}
In this measurement, a passive, 62-\micron-thick silicon target was used as the
target. The silicon target is $5\times5$~\centi\meter$^2$ in area. The muon
In this measurement, a passive, 62-\si{\micro\meter}-thick silicon target was used as the
target. The silicon target is $5\times5$~\si{\centi\meter}$^2$ in area. The muon
momentum was chosen to be 1.06 after a scanning to maximise the stopping ratio.
The charged particles were measured by two arms of silicon detectors. The
plastic scintillators vetoing information were not used.
@@ -754,17 +755,17 @@ tree contains total $1.452 \times 10^8$ muon events. %145212698
\subsection{Particle identification by dE/dx and proton selection}
\label{sub:particle_identification_by_de_dx}
%All silicon hits with energy deposition larger than
%200~\kilo\electronvolt\ that happened within $\pm 10$~\micro\second\ of the
%200~\si{\kilo\electronvolt}\ that happened within $\pm 10$~\si{\micro\second}\ of the
%muon hit are then
%associated to the muon and stored in the muon event tree. The
%200~\kilo\electronvolt\ cut effectively rejects all MIPs hits on thin silicon
%detectors of which the most probable value is about 40~\kilo\electronvolt.
%200~\si{\kilo\electronvolt}\ cut effectively rejects all MIPs hits on thin silicon
%detectors of which the most probable value is about 40~\si{\kilo\electronvolt}.
%In order to use dE/dx for particle identification, $\Delta$E and total E are
%needed.
The charged particle selection starts from searching for muon event
that has at least one hit on thick silicon. If there is a thin silicon hit
within a coincidence window of $\pm 0.5$~\micro\second\ around the thick
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
@@ -786,8 +787,8 @@ $\Delta$E-E plots can be identified as follows:
\end{itemize}
%The electrons either from Michel decay or from the beam are MIPs particles,
%which would deposit about 466~keV on the 1500-\micron-thick silicon detector,
%and about 20~keV on the 65-\micron-thick silicon detector. Therefore our thin
%which would deposit about 466~keV on the 1500-\si{\micro\meter}-thick silicon detector,
%and about 20~keV on the 65-\si{\micro\meter}-thick silicon detector. Therefore our thin
%silicon counters could not distinguish electrons from electronic
%noise. The brightest spots on the $\Delta$E-E plots are identified as electrons
%due to
@@ -864,7 +865,7 @@ The double peaks of muonic X-rays from the lead shield at 431 and 438~keV are
very intense, reflects the fact that the low momentum muon beam of
29.68~MeV\cc\ (scaling factor 1.06) was strongly scattered by the upstream
counters. After a prompt cut that requires the photon
hit occured in $\pm 1$~\micro\second\ around the muon hit, the peaks from lead
hit occured in $\pm 1$~\si{\micro\second}\ around the muon hit, the peaks from lead
remain prominent which is an expected result because of all the lead shield
inside the chamber was to capture stray muons. The cut shows its effect on
reducing the background level under the 400.177 keV peak by about one third.
@@ -872,7 +873,7 @@ reducing the background level under the 400.177 keV peak by about one third.
\begin{figure}[htb]
\centering
\includegraphics[width=0.98\textwidth]{figs/si16p_xray}
\caption{X-ray spectrum from the passive 62-\micron-thick silicon target with
\caption{X-ray spectrum from the passive 62-\si{\micro\meter}-thick silicon target with
and with out timing cut.}
\label{fig:si16_xray}
\end{figure}
@@ -918,10 +919,10 @@ Table~\ref{tab:si16p_ncapture_cal}.
\label{sub:lifetime_measurement}
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~\micro\second\ time steps on the proton
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
curves show decay constants of $762.9 \pm 13.7$~\nano\second\ and $754.6 \pm
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
silicon in the literatures of $758 \pm 2$~\cite{}. This is the confirmation
@@ -941,7 +942,7 @@ 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}.
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~\micron.
range of 2.5~MeV protons in silicon is about 68~\si{\micro\meter}.
\begin{figure}[htb]
\centering
\includegraphics[width=0.85\textwidth]{figs/si16p_proton_ecut_500nstcut}
@@ -1058,7 +1059,7 @@ The ratio between the number of protons and other particles at 500~ns is $(1927
%\centering
%\includegraphics[width=0.85\textwidth]{figs/si16p_toyMC}
%\caption{An example of response function between the observed energy and
%initial energy of protons in a 62-\micron-target.}
%initial energy of protons in a 62-\si{\micro\meter}-target.}
%\label{fig:si16p_toyMC}
%\end{figure}
@@ -1096,7 +1097,7 @@ The ratio between the number of protons and other particles at 500~ns is $(1927
%\subsection{Proton emission rate and uncertainties estimation}
%\label{sub:proton_emission_rate_and_uncertainties_estimation}
%The rate of proton emission from 2.5--10~\mega\electronvolt is:
%The rate of proton emission from 2.5--10~\si{\mega\electronvolt} is:
%\begin{equation}
%R =
%\end{equation}
@@ -1119,7 +1120,7 @@ The ratio between the number of protons and other particles at 500~ns is $(1927
\section{Proton emission following muon capture on an aluminium target}
\label{sec:proton_emission_following_muon_capture_on_an_aluminium_target}
The aluminium is the main object of the AlCap experiment, in this preliminary
analysis I chose one target, Al100 the 100-\micron-thick target, on
analysis I chose one target, Al100 the 100-\si{\micro\meter}-thick target, on
a sub-range of the data set runs 2808--2873, as a demonstration.
Because this is a passive target, the same procedure and cuts used in the
passive silicon runs were applied.
@@ -1163,8 +1164,8 @@ proton energy spectrum is shown in Figure~\ref{fig:al100_proton_spec}.
The lifetime of these protons are shown in
Figure~\ref{fig:al100_proton_lifetime}, the fitted decay constant on the right
arm is consistent with the reference value of $864 \pm 2$~\nano\second~\cite{}.
But the left arm gives $918 \pm 16.1$~\nano\second, significantly larger than
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
@@ -1180,7 +1181,7 @@ the reference value.
Further investigation of the problem of longer lifetime was made and the first
channel on the thin silicon detector on that channel was the offender. The
lifetime measurement with out that SiL1-1 channel gives a reasonable result,
and the decay constant on the SiL1-1 alone was nearly about 1000~\micro\second.
and the decay constant on the SiL1-1 alone was nearly about 1000~\si{\micro\second}.
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