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in progress of adapting things to siunitx, done chap4

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2014-09-07 12:18:11 +09:00
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thesis2/chapters/chap3_comet.tex
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@@ -83,11 +83,11 @@ The most recent experiments were the SINDRUM and SINDRUM-II at the Paul
Scherrer Institute (PSI), Switzerland. The SINDRUM-II measured the branching Scherrer Institute (PSI), Switzerland. The SINDRUM-II measured the branching
ratio of \mueconv on a series of heavy targets: Ti, Pb and Au. The proton beam ratio of \mueconv on a series of heavy targets: Ti, Pb and Au. The proton beam
at PSI is a continuous wave beam, with a time structure of 0.3 ns bursts every at PSI is a continuous wave beam, with a time structure of 0.3 ns bursts every
19.75 \nano\second. An 8-\milli\meter-thick CH$_2$ degrader was used to reduce 19.75 \si{\nano\second}. An 8-\si{\milli\meter}-thick CH$_2$ degrader was used to reduce
the radiative pion capture and other prompt backgrounds. Cosmic backgrounds are the radiative pion capture and other prompt backgrounds. Cosmic backgrounds are
rejected using a combination of rejected using a combination of
passive shielding, veto counters and reconstruction cuts. The momenta of muons passive shielding, veto counters and reconstruction cuts. The momenta of muons
were 52 \mega\electronvolt\per\cc and 53 \mega\electronvolt\per\cc, and the were 52 \si{\mega\electronvolt\per\cc} and 53 \si{\mega\electronvolt\per\cc}, and the
momentum spread was 2\%. momentum spread was 2\%.
\begin{figure}[htbp] \centering \begin{figure}[htbp] \centering
\includegraphics[width=0.85\textwidth]{figs/sindrumII_setup} \includegraphics[width=0.85\textwidth]{figs/sindrumII_setup}
@@ -173,7 +173,7 @@ sensitivity of the COMET experiment. A slow-extracted proton beam from
the J-PARC main ring (MR), which is designed to deliver \sn{3.6}{15} protons per the J-PARC main ring (MR), which is designed to deliver \sn{3.6}{15} protons per
cycle at a frequency of 0.45 Hz, will be used for the COMET experiment. The cycle at a frequency of 0.45 Hz, will be used for the COMET experiment. The
proton beam power of the current design is 8 GeV$\times$7 $\mu$A, or proton beam power of the current design is 8 GeV$\times$7 $\mu$A, or
\sn{4.4}{13} protons/s. The beam energy 8 \giga\electronvolt~ helps to minimise \sn{4.4}{13} protons/s. The beam energy 8 \si{\giga\electronvolt} helps to minimise
the production of antiprotons. the production of antiprotons.
The proton pulse width is chosen to be 100 ns, and the pulse period to be The proton pulse width is chosen to be 100 ns, and the pulse period to be
@@ -196,8 +196,8 @@ Table~\ref{tab:comet_proton_beam}.
\includegraphics[width=0.8\textwidth]{figs/comet_mr_4filled} \includegraphics[width=0.8\textwidth]{figs/comet_mr_4filled}
\caption{The COMET proton bunch structure in the RCS (rapid cycle \caption{The COMET proton bunch structure in the RCS (rapid cycle
synchrotron) and MR where 4 buckets synchrotron) and MR where 4 buckets
are filled producing 100 \nano\second~bunches separated by 1.2 are filled producing 100 \si{\nano\second} bunches separated by
\micro\second.} 1.2~\si{\micro\second}.}
\label{fig:comet_mr_4filled} \label{fig:comet_mr_4filled}
\end{figure} \end{figure}
@@ -205,14 +205,14 @@ Table~\ref{tab:comet_proton_beam}.
\begin{center} \begin{center}
\begin{tabular}{l l} \begin{tabular}{l l}
\toprule \toprule
Beam power & 56 \kilo\watt\\ Beam power & 56 \si{\kilo\watt}\\
Energy & 8 \giga\electronvolt\\ Energy & 8 \si{\giga\electronvolt}\\
Average current & 7 \micro\ampere\\ Average current & 7 \si{\micro\ampere}\\
Beam emittance & 10 $\pi$\cdot mm\cdot mrad\\ Beam emittance & 10 $\pi\cdot$ mm$\cdot$ mrad\\
Protons per bunch & $<10^{11}$\\ Protons per bunch & $<10^{11}$\\
Extinction & \sn{}{-9}\\ Extinction & \sn{}{-9}\\
Bunch separation & $1 \sim 2$ \micro\second\\ Bunch separation & $1 \sim 2$ \si{\micro\second}\\
Bunch length & 100 \nano\second\\ Bunch length & 100 \si{\nano\second}\\
\bottomrule \bottomrule
\end{tabular} \end{tabular}
\end{center} \end{center}
@@ -321,7 +321,7 @@ needed to select 40 MeV/$c$ muons as required by the COMET design.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Muon stopping target} \subsection{Muon stopping target}
\label{sub:muon_stopping_target} \label{sub:muon_stopping_target}
Muon stopping target is place at 180\degree~bending after the pion production Muon stopping target is place at 180\si{\degree}~bending after the pion production
target (Figure~\ref{fig:comet_beamline_layout}) in its own solenoid. The target target (Figure~\ref{fig:comet_beamline_layout}) in its own solenoid. The target
is designed to maximise the muon stopping efficiency and minimise the energy is designed to maximise the muon stopping efficiency and minimise the energy
loss of signal electrons. loss of signal electrons.
@@ -337,7 +337,7 @@ The first choice for the muon stopping target material in the COMET is
aluminium. A titanium target is also considered. Configuration of the target is aluminium. A titanium target is also considered. Configuration of the target is
shown in the Table~\ref{tab:comet_al_target}. Monte Carlo studies with this shown in the Table~\ref{tab:comet_al_target}. Monte Carlo studies with this
design showed that net stopping efficiency is 0.29, and average energy loss design showed that net stopping efficiency is 0.29, and average energy loss
of signal electrons is about 400 \kilo\electronvolt. of signal electrons is about 400 \si{\kilo\electronvolt}.
\begin{table}[htb] \begin{table}[htb]
\begin{center} \begin{center}
\begin{tabular}{l l} \begin{tabular}{l l}
@@ -346,10 +346,10 @@ of signal electrons is about 400 \kilo\electronvolt.
\midrule \midrule
Material & Aluminium\\ Material & Aluminium\\
Shape & Flat disks\\ Shape & Flat disks\\
Disk radius & 100 \milli\meter\\ Disk radius & 100 \si{\milli\meter}\\
Disk thickness & 200 \micro\meter\\ Disk thickness & 200 \si{\micro\meter}\\
Number of disks & 17\\ Number of disks & 17\\
Disk spacing & 50 \milli\meter\\ Disk spacing & 50 \si{\milli\meter}\\
\bottomrule \bottomrule
\end{tabular} \end{tabular}
\end{center} \end{center}
@@ -375,15 +375,15 @@ transport section.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Electron transportation beam line} \subsection{Electron transportation beam line}
\label{sub:electron_transportation_beam_line} \label{sub:electron_transportation_beam_line}
The 180\degree~bending electron transport solenoids help remove line-of-sight The 180\si{\degree}~bending electron transport solenoids help remove line-of-sight
between the target and the detector system. It works similarly to the muon between the target and the detector system. It works similarly to the muon
transportation section, but is tuned differently to accept electrons of about transportation section, but is tuned differently to accept electrons of about
105 \mega\electronvolt\per\cc. A compensation field of 0.17 T along the 105~\si{\mega\electronvolt\per\cc}. A compensation field of 0.17 T along the
vertical direction will be applied. Electrons with momentum less than 80 vertical direction will be applied. Electrons with momentum less than 80
\mega\electronvolt\per\cc are blocked at the exit of this section by \si{\mega\electronvolt\per\cc} are blocked at the exit of this section by
a collimator to reduce DIO electrons rate. The net acceptance of signals of a collimator to reduce DIO electrons rate. The net acceptance of signals of
\mueconv is about 0.32, and the detector hit rate will be in the order of \mueconv is about 0.32, and the detector hit rate will be in the order of
1 \kilo\hertz~for \sn{}{11} stopped muons\per\second. 1~\si{\kilo\hertz}~for \sn{}{11} stopped muons\si{\per\second}.
% subsection electron_transportation_beam_line (end) % subsection electron_transportation_beam_line (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Electron detectors} \subsection{Electron detectors}
@@ -396,13 +396,14 @@ particles, and measure their momenta, energy and timings. The whole detector
system is in a uniform solenoidal magnetic field under vacuum. Passive and system is in a uniform solenoidal magnetic field under vacuum. Passive and
active shielding against cosmic rays is considered. active shielding against cosmic rays is considered.
The tracking detector has to provide a momentum resolution less than 350 The tracking detector has to provide a momentum resolution less than
\kilo\electronvolt\per\cc in order to achieve a sensitivity of \sn{3}{-17}. 350~\si{\kilo\electronvolt\per\cc} in order to achieve a sensitivity of
There are five stations of straw-tube gas chambers, each provides two \sn{3}{-17}. There are five stations of straw-tube gas chambers, each provides
dimensional information. Each straw tube is 5 \milli\meter in diameter and has two
a 25 \micro\meter-thick wall. According to a GEANT4 Monte Carlo simulation, dimensional information. Each straw tube is 5~\si{\milli\meter} in diameter and has
a position resolution of 250 \micro\meter can be obtained, which is enough for a 25~\si{\micro\meter}-thick wall. According to a GEANT4 Monte Carlo simulation,
350 \kilo\electronvolt\per\cc momentum resolution. The DIO background of 0.15 a position resolution of 250~\si{\micro\meter} can be obtained, which is enough for
350~\si{\kilo\electronvolt\per\cc} momentum resolution. The DIO background of 0.15
events is estimated. events is estimated.
The electromagnetic calorimeter serves three purposes: a) to measure electrons The electromagnetic calorimeter serves three purposes: a) to measure electrons
@@ -418,14 +419,14 @@ hit positions. Two candidate crystals, GSO and LYSO, are under consideration.
The requirements for \mueconv signals are: The requirements for \mueconv signals are:
\begin{itemize} \begin{itemize}
\item from the 350 \kilo\electronvolt\per\cc~momentum resolution, the signal \item from the 350~\si{\kilo\electronvolt\per\cc}~momentum resolution, the signal
region is determined to be 103.5 \mega\electronvolt\per\cc~to 105.2 region is determined to be 103.5~\si{\mega\electronvolt\per\cc}~to
\mega\electronvolt\per\cc; 105.2~\si{\mega\electronvolt\per\cc};
\item transversal momentum of signal electrons is required to be greater than \item transversal momentum of signal electrons is required to be greater than
52 \mega\electronvolt\per\cc to remove backgrounds from beam electrons and 52~\si{\mega\electronvolt\per\cc} to remove backgrounds from beam electrons and
muons decay in flight; muons decay in flight;
\item timing wise, conversion electrons should arrive in the time window of \item timing wise, conversion electrons should arrive in the time window of
detection which is about 700 \nano\second~after each proton pulses detection which is about 700~\si{\nano\second}~after each proton pulses
(Figure~\ref{fig:comet_meas_timing}). The acceptance in this detection (Figure~\ref{fig:comet_meas_timing}). The acceptance in this detection
window is about 0.39 for aluminium. window is about 0.39 for aluminium.
\end{itemize} \end{itemize}
@@ -449,7 +450,7 @@ The single event sensitivity (SES) of the \mueconv search is defined as:
where $N^{\textrm{stop}}_{\mu}$ is the number of muons stopping in the muon where $N^{\textrm{stop}}_{\mu}$ is the number of muons stopping in the muon
target; $f_{\textrm{cap}}$ is the fraction of captured muons; and $A_e$ is the target; $f_{\textrm{cap}}$ is the fraction of captured muons; and $A_e$ is the
detector acceptance. The total number of stopped muons is projected as detector acceptance. The total number of stopped muons is projected as
$N^{\textrm{stop}}_{\mu} = 2\times 10^{18}$ for a \sn{2}{7}\second~run time; $N^{\textrm{stop}}_{\mu} = 2\times 10^{18}$ for a \sn{2}{7}\si{\second}~run time;
$f_{\textrm{cap}} = 0.61$ for aluminium; and the total acceptance for the COMET $f_{\textrm{cap}} = 0.61$ for aluminium; and the total acceptance for the COMET
detector system is $A_e =0.031$. Using these detector system is $A_e =0.031$. Using these
numbers, the SES of the COMET is calculated to be numbers, the SES of the COMET is calculated to be
@@ -519,7 +520,7 @@ the ultimate COMET experiment, and initial phase is desirable. Also, the 5-year
mid-term plan from 2013 of J-PARC includes the construction of the COMET beam mid-term plan from 2013 of J-PARC includes the construction of the COMET beam
line. For these reasons, the COMET collaboration considers a staged approach line. For these reasons, the COMET collaboration considers a staged approach
with the first stage, so called COMET Phase-I, with a shorter muon with the first stage, so called COMET Phase-I, with a shorter muon
transportation solenoid, up to the first 90\degree. transportation solenoid, up to the first 90\si{\degree}.
%\begin{wrapfigure}{r}{0.5\textwidth} %\begin{wrapfigure}{r}{0.5\textwidth}
%\centering %\centering
@@ -531,7 +532,7 @@ transportation solenoid, up to the first 90\degree.
\begin{SCfigure} \begin{SCfigure}
\centering \centering
\caption{Lay out of the COMET Phase-I, the target and detector solenoid are \caption{Lay out of the COMET Phase-I, the target and detector solenoid are
placed after the first 90\degree~bend.} placed after the first 90\si{\degree}~bend.}
\includegraphics[width=0.4\textwidth]{figs/comet_phase1_layout} \includegraphics[width=0.4\textwidth]{figs/comet_phase1_layout}
\label{fig:comet_phase1_layout} \label{fig:comet_phase1_layout}
\end{SCfigure} \end{SCfigure}
@@ -556,11 +557,11 @@ The COMET Phase-I has two major goals:
\label{sub:proton_beam_for_the_comet_phase_i} \label{sub:proton_beam_for_the_comet_phase_i}
Proton beam for the Phase-I differs only in beam power compares to that of the Proton beam for the Phase-I differs only in beam power compares to that of the
full COMET. It is estimated that a beam power of full COMET. It is estimated that a beam power of
3.2~\kilo\watt~$=$~8~\giga\electronvolt~$\times$~0.4~\micro\ampere~(or 3.2~\si{\kilo\watt}~$=$~8~\si{\giga\electronvolt}~$\times$~0.4~\si{\micro\ampere}~(or
\sn{2.5}{12} protons\per\second) will be enough for beam properties \sn{2.5}{12} protons\si{\per\second}) will be enough for beam properties
study and achieving the physics goal of this stage. study and achieving the physics goal of this stage.
Starting from a lower intensity is also suitable for performing accelerator Starting from a lower intensity is also suitable for performing accelerator
studies that are needed to realise 8 \giga\electronvolt beam extraction from studies that are needed to realise 8~\si{\giga\electronvolt} beam extraction from
the J-PARC main ring. the J-PARC main ring.
% subsection proton_beam_for_the_comet_phase_i (end) % subsection proton_beam_for_the_comet_phase_i (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -570,14 +571,14 @@ the J-PARC main ring.
Since the beam power will be lower, it is proposed to use a graphite target in Since the beam power will be lower, it is proposed to use a graphite target in
the Phase-I. This will minimise the activation of the target station and heat the Phase-I. This will minimise the activation of the target station and heat
shield which will be easier for necessary upgrading for Phase-II operation. shield which will be easier for necessary upgrading for Phase-II operation.
A target length of 600 \milli\meter~(1.5 radiation length) and target radius of A target length of 600~\si{\milli\meter}~(1.5 radiation length) and target radius of
20 \milli\meter~are chosen. The target is located at the centre of the pion 20~\si{\milli\meter}~are chosen. The target is located at the centre of the pion
capture solenoid where the peak magnetic field of 5 T is achieved. capture solenoid where the peak magnetic field of 5 T is achieved.
A correction dipole filed of 0.05 T is also applied to improve the pion yield. A correction dipole filed of 0.05 T is also applied to improve the pion yield.
The pion/muon beam line for COMET Phase-I consists of the pion capture solenoid The pion/muon beam line for COMET Phase-I consists of the pion capture solenoid
section (CS), muon transport solenoid section (TS) up to the first section (CS), muon transport solenoid section (TS) up to the first
90\degree~bending, and a set of matching solenoids (see 90\si{\degree}~bending, and a set of matching solenoids (see
Figure~\ref{fig:comet_phase1_magnets}). At the end of the muon beam line, the Figure~\ref{fig:comet_phase1_magnets}). At the end of the muon beam line, the
detectors and the detector solenoid (DS) are installed. To reduce beam detectors and the detector solenoid (DS) are installed. To reduce beam
backgrounds, a beam collimator is placed upstream of the detector solenoid. backgrounds, a beam collimator is placed upstream of the detector solenoid.
@@ -623,45 +624,47 @@ reduce potential high rates caused by protons emitted after nuclear muon
capture in the stopping target. capture in the stopping target.
The CDC covers the region The CDC covers the region
from 500 \milli\meter~to 831 \milli\meter~in the radial direction. The length from \SIrange{500}{831}{\milli\meter}~in the radial direction. The length
of the CDC is 1500 \milli\meter. The inner wall is made of a 100 of the CDC is 1500~\si{\milli\meter}. The inner wall is made of
\micro\meter~thick aluminised Mylar. The end-plates will be conical in shape a 100~\si{\micro\meter}-thick aluminised Mylar. The end-plates will be conical
and about 10 \milli\meter~thick to support the feedthroughs. The outer wall is in shape and about 10~\si{\milli\meter}-thick to support the feedthroughs. The outer
made of 5 \milli\meter~carbon fibre reinforced plastic (CFRP). wall is
made of 5~\si{\milli\meter}~carbon fibre reinforced plastic (CFRP).
The CDC is arranged in 20 concentric sense layers with alternating positive and The CDC is arranged in 20 concentric sense layers with alternating positive and
negative stereo angles. The sense wires are made of gold-plated tungsten, 30 negative stereo angles. The sense wires are made of gold-plated tungsten,
\micro\meter~in diameter, tensioned to 50 \gram. The field wires are uncoated 30~\si{\micro\meter} in diameter, tensioned to 50~\si{\gram}. The field wires
aluminium wires with a diameter of 80 \micro\meter, at the same tension of 50 are uncoated aluminium wires with a diameter of 80~\si{\micro\meter}, at the same
\gram. A high voltage of $1700\sim1900$ \volt~will be applied to the sense tension of \SI{50}{\gram}. A high voltage of $1700\sim1900$~\si{\volt} will be
wires with the field wires at ground potential, giving an avalanche gain of applied to the sense wires with the field wires at ground potential, giving an
avalanche gain of
approximately \sn{4}{4}. A gas mixture of helium:isobutane(90:10) is preferred approximately \sn{4}{4}. A gas mixture of helium:isobutane(90:10) is preferred
since the CDC momentum resolution is dominated by multiple scattering. With since the CDC momentum resolution is dominated by multiple scattering. With
these configurations, an intrinsic momentum resolution of 197 these configurations, an intrinsic momentum resolution of
\kilo\electronvolt\per\cc~is achievable according to our tracking study. 197~\si{\kilo\electronvolt\per\cc} is achievable according to our tracking study.
\begin{table}[htb] \begin{table}[htb]
\begin{center} \begin{center}
\begin{tabular}{l l l} \begin{tabular}{l l l}
\toprule \toprule
\textbf{Inner wall} & Length & 1500 \milli\meter\\ \textbf{Inner wall} & Length & 1500 \si{\milli\meter}\\
& Radius & 500 \milli\meter\\ & Radius & 500 \si{\milli\meter}\\
\midrule \midrule
\textbf{Outer wall} & Length & 1740.9 \milli\meter\\ \textbf{Outer wall} & Length & 1740.9 \si{\milli\meter}\\
& Radius & 831 \milli\meter\\ & Radius & 831 \si{\milli\meter}\\
\midrule \midrule
\textbf{Sense wire} & Number of layers & 20\\ \textbf{Sense wire} & Number of layers & 20\\
& Material & Gold-plated tungsten\\ & Material & Gold-plated tungsten\\
& Diameter & 30 \micro\meter\\ & Diameter & 30 \si{\micro\meter}\\
& Number of wires & 4986\\ & Number of wires & 4986\\
& Tension & 50 \gram\\ & Tension & 50 \si{\gram}\\
%& Radius of the innermost wire at the EP & 530 mm\\ %& Radius of the innermost wire at the EP & 530 mm\\
%& Radius of the outermost wire at the EP & 802 mm\\ %& Radius of the outermost wire at the EP & 802 mm\\
\midrule \midrule
\textbf{Field wire} & Material & Aluminium\\ \textbf{Field wire} & Material & Aluminium\\
& Diameter & 80 \micro\meter\\ & Diameter & 80 \si{\micro\meter}\\
& Number of wires & 14562\\ & Number of wires & 14562\\
& Tension & 50 \gram\\ & Tension & 50 \si{\gram}\\
\midrule \midrule
\textbf{Gas} & & Helium:Isobutane (90:10)\\ \textbf{Gas} & & Helium:Isobutane (90:10)\\
\bottomrule \bottomrule
@@ -673,11 +676,12 @@ these configurations, an intrinsic momentum resolution of 197
The maximum usable muon beam intensity will be limited by the detector hit The maximum usable muon beam intensity will be limited by the detector hit
occupancy. Charge particles with transversal momentum greater than 70 occupancy. Charge particles with transversal momentum greater than 70
\mega\electronvolt\per\cc~are expected to reach the CDC. Those particles are: \si{\mega\electronvolt\per\cc} are expected to reach the CDC. Those particles are:
protons emitted from nuclear muon capture, and electrons from muon decay in protons emitted from nuclear muon capture, and electrons from muon decay in
orbit. It is calculated that the hit rate due to proton emission dominates, orbit. It is calculated that the hit rate due to proton emission dominates,
where the highest rate is 11 \kilo\hertz\per cell compares to 5 \kilo\hertz\per where the highest rate is 11~\si{\kilo\hertz\per}cell compares to
cell contribution from DIO electrons. Another potential issue caused by protons 5~\si{\kilo\hertz\per}
cell contributing from DIO electrons. Another potential issue caused by protons
is the ageing effect on the CDC as they leave about a 100 times larger is the ageing effect on the CDC as they leave about a 100 times larger
energy deposit than the minimum ionisation particles. energy deposit than the minimum ionisation particles.
@@ -687,8 +691,9 @@ of protons emitted after muon capture in aluminium. In the design of the COMET
Phase-I, we use a conservative estimation of the rate of protons from energy Phase-I, we use a conservative estimation of the rate of protons from energy
spectrum of charged particles emitted from muon capture in spectrum of charged particles emitted from muon capture in
$^{28}$Si~\cite{SobottkaWills.1968}. The baseline design for the proton $^{28}$Si~\cite{SobottkaWills.1968}. The baseline design for the proton
absorber is 1.0 \milli\meter~thick CFRP, which contributes 195 absorber is 1.0~\si{\milli\meter}-thick CFRP, which contributes
\kilo\electronvolt\per\cc~to the momentum resolution of reconstructed track. 195~\si{\kilo\electronvolt\per\cc} to the momentum resolution of reconstructed
track.
In order to obtain a better understanding of the protons emission, and then In order to obtain a better understanding of the protons emission, and then
further optimisation of the CDC, a dedicated experiment to measure proton further optimisation of the CDC, a dedicated experiment to measure proton

32
thesis2/chapters/chap4_alcap_phys.tex
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@@ -66,17 +66,17 @@ emission of particles with emphasis on proton.
Theoretically, the capturing process can be described in the following Theoretically, the capturing process can be described in the following
stages~\cite{FermiTeller.1947, WuWilets.1969}: stages~\cite{FermiTeller.1947, WuWilets.1969}:
\begin{enumerate} \begin{enumerate}
\item High to low (a few \kilo\electronvolt) energy: the muon velocity are \item High to low (a few \si{\kilo\electronvolt}) energy: the muon velocity are
greater than the velocity of the valence electrons of the atom. Slowing greater than the velocity of the valence electrons of the atom. Slowing
down process is similar to that of fast heavy charged particles. It takes down process is similar to that of fast heavy charged particles. It takes
about \sn{}{-9} to \sn{}{-10} \second~to slow down from a relativistic about \sn{}{-9} to \sn{}{-10} \si{\second}~to slow down from a relativistic
\sn{}{8} \electronvolt~energy to 2000 \electronvolt~in condensed matter, \sn{}{8}~\si{\electronvolt}~energy to 2000~\si{\electronvolt}~in condensed matter,
and about 1000 times as long in air. and about 1000 times as long in air.
\item Low energy to rest: in this phase, the muon velocity is less than that \item Low energy to rest: in this phase, the muon velocity is less than that
of the valence electrons, the muon is considered to be moving inside of the valence electrons, the muon is considered to be moving inside
a degenerate electron gas. The muon rapidly comes to a stop either in a degenerate electron gas. The muon rapidly comes to a stop either in
condensed matters ($\sim$\sn{}{-13} \second) or in gases ($\sim$\sn{}{-9} condensed matters ($\sim$\sn{}{-13}~\si{\second}) or in gases ($\sim$\sn{}{-9}
\second). \si{\second}).
\item Atomic capture: the muon has no kinetic energy, it is captured by the \item Atomic capture: the muon has no kinetic energy, it is captured by the
host atom into one of high orbital states, forming a muonic atom. The host atom into one of high orbital states, forming a muonic atom. The
distribution of initial states is not well known. The details depend on distribution of initial states is not well known. The details depend on
@@ -86,9 +86,9 @@ stages~\cite{FermiTeller.1947, WuWilets.1969}:
by the emission of Auger electrons or characteristic X-rays, or excitation by the emission of Auger electrons or characteristic X-rays, or excitation
of the nucleus. The time taken for the muon to enter the lowest possible of the nucleus. The time taken for the muon to enter the lowest possible
state, 1S, from the instant of its atomic capture is state, 1S, from the instant of its atomic capture is
$\sim$\sn{}{-14}\second. $\sim$\sn{}{-14}\si{\second}.
\item Muon disappearance: after reaching the 1S state, the muons either \item Muon disappearance: after reaching the 1S state, the muons either
decays with a half-life of \sn{2.2}{-6} \second~or gets captured by the decays with a half-life of \sn{2.2}{-6}~\si{\second}~or gets captured by the
nucleus. In hydrogen, the capture to decay probability ratio is about nucleus. In hydrogen, the capture to decay probability ratio is about
\sn{4}{-4}. Around $Z=11$, the capture probability is roughly equal to the \sn{4}{-4}. Around $Z=11$, the capture probability is roughly equal to the
decay probability. In heavy nuclei ($Z\sim50$), the ratio of capture to decay probability. In heavy nuclei ($Z\sim50$), the ratio of capture to
@@ -98,7 +98,7 @@ stages~\cite{FermiTeller.1947, WuWilets.1969}:
than a K-shell electron. The close proximity of the K-shell muon in the than a K-shell electron. The close proximity of the K-shell muon in the
Coulomb field of a nuclear, together with its weak interaction with the Coulomb field of a nuclear, together with its weak interaction with the
nucleus, allows the muon to spend a significant fraction of time (\sn{}{-7} nucleus, allows the muon to spend a significant fraction of time (\sn{}{-7}
-- \sn{}{-6} \second) within the nucleus, serving as an ideal probe for the -- \sn{}{-6} \si{\second}) within the nucleus, serving as an ideal probe for the
distribution of nuclear charge and nuclear moments. distribution of nuclear charge and nuclear moments.
\end{enumerate} \end{enumerate}
@@ -307,7 +307,7 @@ and of course not perfect, description of the existing data~\cite{Measday.2001}:
- X_2\left(\frac{A-Z}{2A}\right)\right] - X_2\left(\frac{A-Z}{2A}\right)\right]
\label{eq:primakoff_capture_rate} \label{eq:primakoff_capture_rate}
\end{equation} \end{equation}
where $X_1 = 170$ \reciprocal\second~is the muon capture rate for hydrogen, but where $X_1 =$ \SI{170}{\second^{-1}}~is the muon capture rate for hydrogen, but
reduced because a smaller phase-space in the nuclear muon capture compares to reduced because a smaller phase-space in the nuclear muon capture compares to
that of a nucleon; and $X_2 = 3.125$ takes into account the fact that it is that of a nucleon; and $X_2 = 3.125$ takes into account the fact that it is
harder for protons to transforms into neutrons due to the Pauli exclusion harder for protons to transforms into neutrons due to the Pauli exclusion
@@ -347,20 +347,20 @@ $n_{avg} = (0.3 \pm 0.02)A^{1/3}$~\cite{Singer.1974}.
The neutron emission can be explained by several mechanisms: The neutron emission can be explained by several mechanisms:
\begin{enumerate} \begin{enumerate}
\item Direct emission follows reaction~\eqref{eq:mucap_proton}: these neutrons \item Direct emission follows reaction~\eqref{eq:mucap_proton}: these neutrons
have fairly high energy, from a few \mega\electronvolt~to as high as 40--50 have fairly high energy, from a few \si{\mega\electronvolt}~to as high as 40--50
\mega\electronvolt. \si{\mega\electronvolt}.
\item Indirect emission through an intermediate compound nucleus: the energy \item Indirect emission through an intermediate compound nucleus: the energy
transferred to the neutron in the process~\eqref{eq:mucap_proton} is 5.2 transferred to the neutron in the process~\eqref{eq:mucap_proton} is 5.2
\mega\electronvolt~if the initial proton is at rest, in nuclear \si{\mega\electronvolt} if the initial proton is at rest, in nuclear
environment, protons have a finite momentum distribution, therefore the environment, protons have a finite momentum distribution, therefore the
mean excitation energy of the daughter nucleus is around 15 to 20 mean excitation energy of the daughter nucleus is around 15 to 20
\mega\electronvolt~\cite{Mukhopadhyay.1977}. This is above the nucleon \si{\mega\electronvolt}~\cite{Mukhopadhyay.1977}. This is above the nucleon
emission threshold in all complex nuclei, thus the daughter nucleus can emission threshold in all complex nuclei, thus the daughter nucleus can
de-excite by emitting one or more neutrons. In some actinide nuclei, that de-excite by emitting one or more neutrons. In some actinide nuclei, that
excitation energy might trigger fission reactions. The energy of indirect excitation energy might trigger fission reactions. The energy of indirect
neutrons are mainly in the lower range $E_n \le 10$ \mega\electronvolt~with neutrons are mainly in the lower range $E_n \le 10$ \si{\mega\electronvolt}
characteristically exponential shape of evaporation process. On top of that with characteristically exponential shape of evaporation process. On top of
are prominent lines might appear where giant resonances occur. that are prominent lines might appear where giant resonances occur.
\end{enumerate} \end{enumerate}
Experimental measurement of neutron energy spectrum is technically hard, and it Experimental measurement of neutron energy spectrum is technically hard, and it
is difficult to interpret the results. Due to these difficulties, only a few is difficult to interpret the results. Due to these difficulties, only a few

6
thesis2/thesis.tex
View File

@@ -31,7 +31,11 @@ for the COMET experiment}
\mainmatter \mainmatter
\input{chapters/chap1_intro} \input{chapters/chap1_intro}
\input{chapters/chap2_mu_e_conv} \input{chapters/chap2_mu_e_conv}
\lipsum[1-15] %\input{chapters/chap3_comet}
%\input{chapters/chap4_alcap_phys}
%\input{chapters/chap5_alcap_setup}
%\input{chapters/chap6_analysis}
%\input{chapters/chap7_results}
\begin{backmatter} \begin{backmatter}
\input{chapters/backmatter} \input{chapters/backmatter}