diff --git a/thesis/chapters/chap4_alcap_phys.tex b/thesis/chapters/chap4_alcap_phys.tex
index a5bd278..0501d5b 100644
--- a/thesis/chapters/chap4_alcap_phys.tex
+++ b/thesis/chapters/chap4_alcap_phys.tex
@@ -347,18 +347,18 @@ $n_{avg} = (0.3 \pm 0.02)A^{1/3}$~\cite{Singer.1974}.
 The neutron emission can be explained by several mechanisms:
 \begin{enumerate}
   \item Direct emission follows reaction~\eqref{eq:mucap_proton}: these neutrons
-    have fairly high energy, from a few \si{\mega\electronvolt}~to as high as 40--50
-    \si{\mega\electronvolt}. 
+    have fairly high energy, from a few \si{\si{\MeV}}~to as high as 40--50
+    \si{\si{\MeV}}. 
   \item Indirect emission through an intermediate compound nucleus: the energy
     transferred to the neutron in the process~\eqref{eq:mucap_proton} is 5.2
-    \si{\mega\electronvolt} if the initial proton is at rest, in nuclear
+    \si{\si{\MeV}} if the initial proton is at rest, in nuclear
     environment, protons have a finite momentum distribution, therefore the
     mean excitation energy of the daughter nucleus is around 15 to 20
-    \si{\mega\electronvolt}~\cite{Mukhopadhyay.1977}. This is above the nucleon
+    \si{\si{\MeV}}~\cite{Mukhopadhyay.1977}. This is above the nucleon
     emission threshold in all complex nuclei, thus the daughter nucleus can
     de-excite by emitting one or more neutrons. In some actinide nuclei, that
     excitation energy might trigger fission reactions. The energy of indirect
-    neutrons are mainly in the lower range $E_n \le 10$ \si{\mega\electronvolt}
+    neutrons are mainly in the lower range $E_n \le 10$ \si{\si{\MeV}}
     with characteristically exponential shape of evaporation process. On top of
     that are prominent lines might appear where giant resonances occur.
 \end{enumerate}
@@ -382,7 +382,7 @@ data. There are two reasons for that:
     neutron emission. The rate is about 15\% for light nuclei and
 		reduces to a few percent for medium and heavy nuclei.
 		\item The charged particles are short ranged: the emitted protons,
-		deuterons and alphas are typically low energy (2--20~\mega\electronvolt).
+      deuterons and alphas are typically low energy ( \SIrange{2}{20}{\MeV}).
 		But a relatively thick target is normally needed in order to achieve
 		a reasonable muon stopping rate and charged particle statistics. Therefore,
 		emulsion technique is particularly powerful.
@@ -411,9 +411,9 @@ statistics and in fair agreement with Morigana and Fry
 Protons with higher energy are technically easier to measure, but because of
 the much lower rate, they can only be studied at meson facilities.  Krane and
 colleagues~\cite{KraneSharma.etal.1979} measured proton emission from
-aluminium, copper and lead in the energy range above 40 \mega\electronvolt~and
+aluminium, copper and lead in the energy range above \SI{40}{\MeV} and
 found a consistent exponential shape in all targets.  The integrated yields
-above 40 \mega\electronvolt~are in the \sn{}{-4}--\sn{}{-3} range (see
+above \SI{40}{\MeV} are in the \sn{}{-4}--\sn{}{-3} range (see
 Table~\ref{tab:krane_proton_rate}), a minor contribution to total proton
 emission rate. 
 \begin{table}[htb]
@@ -462,16 +462,16 @@ The aforementioned difficulties in charged particle measurements could be
 solved using an active target, just like nuclear emulsion. Sobottka and
 Wills~\cite{SobottkaWills.1968} took this approach when using a Si(Li) detector
 to stop muons. They obtained a spectrum of charged particles up to 26
-\mega\electronvolt~in Figure~\ref{fig:sobottka_spec}. The peak below 1.4
-\mega\electronvolt~is due to the recoiling $^{27}$Al. The higher energy events
+\si{\MeV}~in Figure~\ref{fig:sobottka_spec}. The peak below 1.4
+\si{\MeV}~is due to the recoiling $^{27}$Al. The higher energy events
 including protons, deuterons and alphas constitute $(15\pm 2)\%$ of capture
 events, which is consistent with a rate of $(12.9\pm1.4)\%$ from gelatine
 observed by Morigana and Fry. This part has an exponential
-decay shape with a decay constant of 4.6 \mega\electronvolt. Measday
+decay shape with a decay constant of 4.6 \si{\MeV}. Measday
 noted~\cite{Measday.2001} the fractions of events in
-the 26--32 \mega\electronvolt~range being 0.3\%, and above 32
-\mega\electronvolt~range being 0.15\%. This figure is in agreement with the
-integrated yield above 40 \mega\electronvolt~from Krane et al.
+the 26--32 \si{\MeV}~range being 0.3\%, and above 32
+\si{\MeV}~range being 0.15\%. This figure is in agreement with the
+integrated yield above 40 \si{\MeV}~from Krane et al.
 
 In principle, the active target technique could be applied to other material
 such as germanium, sodium iodine, caesium iodine, and other scintillation
@@ -480,7 +480,7 @@ identification like in nuclear emulsion, the best one can achieve after all
 corrections is a sum of all charged particles. It should be noted here
 deuterons can contribute significantly, Budyashov et
 al.~\cite{BudyashovZinov.etal.1971} found deuteron components to be
-$(34\pm2)\%$ of the charged particle yield above 18 \mega\electronvolt~in
+$(34\pm2)\%$ of the charged particle yield above 18 \si{\MeV}~in
 silicon, and $(17\pm4)\%$ in copper. 
 \begin{figure}[htb]
   \centering
@@ -547,7 +547,7 @@ protons were taken.
 
 Wyttenbach et al.\ saw that the cross section of each reaction decreases
 exponentially with increasing Coulomb barrier. The decay constant for all
-$(\mu^-,\nu pxn)$ is about 1.5 per \mega\electronvolt~of Coulomb barrier. They
+$(\mu^-,\nu pxn)$ is about 1.5 per \si{\MeV}~of Coulomb barrier. They
 also commented a ratio for different de-excitation channels: 
 \begin{equation}
   (\mu^-,\nu p):(\mu^-,\nu pn):(\mu^-,\nu p2n):(\mu^-,\nu p3n) = 1:6:4:4,
@@ -572,7 +572,7 @@ nucleus is formed, and then it releases energy by statistical emission of
 various particles. Three models for  momentum distribution of protons in the
 nucleus were used: (I) the Chew-Goldberger distribution 
 $\rho(p) \sim A/(B^2 + p^2)^2$; (II) Fermi gas at zero temperature; and (III)
-Fermi gas at a finite temperature ($kT = 9$ \mega\electronvolt).
+Fermi gas at a finite temperature ($kT = 9$ \si{\MeV}).
 
 A very good agreement with the experimental result for the alpha emission was
 obtained with distribution (III), both in the absolute percentage and the energy
@@ -598,7 +598,7 @@ the nucleon, the average excitation energy will increase, but the proton
 emission rate does not significantly improve and still could not explain the
 large discrepancy. He concluded that the evaporation mechanism can account
 for only a small fraction of emitted protons. Moreover, the high energy protons
-of 25--50 \mega\electronvolt~cannot be explained by the evaporation mechanism.
+of 25--50 \si{\MeV}~cannot be explained by the evaporation mechanism.
 He and Lifshitz~\cite{LifshitzSinger.1978, LifshitzSinger.1980} proposed two
 major corrections to Ishii's model: 
 \begin{enumerate}
@@ -611,14 +611,14 @@ major corrections to Ishii's model:
     is possibility for particles to escape from the nucleus. 
 \end{enumerate}
 With these improvements, the calculated proton spectrum agreed reasonably with
-data from Morigana and Fry in the energy range $E_p \le 30$ \mega\electronvolt.
+data from Morigana and Fry in the energy range $E_p \le 30$ \si{\MeV}.
 Lifshitz and Singer noted the pre-equilibrium emission is more important for
 heavy nuclei. Its contribution in light nuclei is about a few percent,
 increasing to several tens of percent for $100<A<180$, then completely
 dominating in very heavy nuclei. This trend is also seen in other nuclear
 reactions at similar excitation energies. The pre-equilibrium emission also
 dominates the higher-energy part, although it falls short at energies higher
-than 30 \mega\electronvolt. The comparison between the calculated proton
+than 30 \si{\MeV}. The comparison between the calculated proton
 spectrum and experimental data is shown in
 Fig.~\ref{fig:lifshitzsinger_cal_proton}.
 \begin{figure}[htb]
@@ -670,7 +670,7 @@ higher than average, though not as high as Vil'gel'mora et
 al.~\cite{VilgelmovaEvseev.etal.1971} observed. 
 
 For protons with higher energies in the range of
-40--90 \mega\electronvolt~observed in the emulsion data as well as in later
+40--90 \si{\MeV}~observed in the emulsion data as well as in later
 experiments~\cite{BudyashovZinov.etal.1971,BalandinGrebenyuk.etal.1978,
 KraneSharma.etal.1979}, Lifshitz and Singer~\cite{LifshitzSinger.1988}
 suggested another contribution from capturing on correlated two-nucleon
@@ -700,7 +700,7 @@ smaller in cases of Al and Cu, and about 10 times higher in case of AgBr
     \end{tabular}
   \end{center}
   \caption{Probability of proton emission with $E_p \ge 40$
-    \mega\electronvolt~as calculated by Lifshitz and
+    \si{\MeV}~as calculated by Lifshitz and
     Singer~\cite{LifshitzSinger.1988} in comparison with available data.}
   \label{tab:lifshitzsinger_cal_proton_rate_1988}
 \end{table}
@@ -710,17 +710,17 @@ smaller in cases of Al and Cu, and about 10 times higher in case of AgBr
 \label{sub:summary_on_proton_emission_from_aluminium}
 There is no direct measurement of proton emission following
 muon capture in the relevant energy for the COMET Phase-I of 2.5--10
-\mega\electronvolt: 
+\si{\MeV}: 
 \begin{enumerate}
   \item Spectrum wise, only one energy spectrum (Figure~\ref{fig:krane_proton_spec})
-    for energies above 40 \mega\electronvolt~is available from Krane et
+    for energies above 40 \si{\MeV}~is available from Krane et
     al.~\cite{KraneSharma.etal.1979},
     where an exponential decay shape with a decay constant of 
-    $7.5 \pm 0.4$~\mega\electronvolt. At low energy range, the best one can get is
+    $7.5 \pm 0.4$~\si{\MeV}. At low energy range, the best one can get is
     the charged particle spectrum, which includes protons, deuterons and alphas,
     from the neighbouring element silicon (Figure~\ref{fig:sobottka_spec}).
-    This charged particle spectrum peaks around 2.5 \mega\electronvolt~and
-    reduces exponentially with a decay constant of 4.6 \mega\electronvolt.
+    This charged particle spectrum peaks around 2.5 \si{\MeV}~and
+    reduces exponentially with a decay constant of 4.6 \si{\MeV}.
   \item The activation data from Wyttenbach et
     al.~\cite{WyttenbachBaertschi.etal.1978} only gives rate of
     $^{27}\textrm{Al}(\mu^-,\nu pn)^{25}\textrm{Na}$ reaction, and set a lower
@@ -748,9 +748,9 @@ A spectrum shape at this energy range is not available.
 \label{sub:motivation_of_the_alcap_experiment}
 As mentioned, protons from muon capture on aluminium might cause a very high
 rate in the COMET Phase-I CDC. The detector is designed to accept particles
-with momenta in the range of 75--120 \mega\electronvolt\per\cc.
+with momenta in the range of 75--120 \si{\MeV\per\cc}.
 Figure~\ref{fig:proton_impact_CDC} shows that protons with kinetic energies of
-2.5--8 \mega\electronvolt~will hit the CDC. Such events are troublesome due to
+2.5--8 \si{\MeV}~will hit the CDC. Such events are troublesome due to
 their large energy deposition. Deuterons and alphas at that momentum range is
 not of concern because they have lower kinetic energy and higher stopping
 power, thus are harder to escape the muon stopping target.
@@ -758,9 +758,9 @@ power, thus are harder to escape the muon stopping target.
   \centering
     \includegraphics[width=0.85\textwidth]{figs/proton_impact_CDC}
   \caption{Momentum-kinetic energy relation of protons, deuterons and alphas
-  below 10\mega\electronvolt. Shaded area is the acceptance of the COMET
+  below 10\si{\MeV}. Shaded area is the acceptance of the COMET
 Phase-I's CDC. Protons with energies in the range of 2.5--8
-\mega\electronvolt~are in the acceptance of the CDC. Deuterons and alphas at
+\si{\MeV}~are in the acceptance of the CDC. Deuterons and alphas at
 low energies should be stopped inside the muon stopping target.}
   \label{fig:proton_impact_CDC}
 \end{figure}
@@ -793,10 +793,10 @@ function given by:
 where $T$ is the kinetic energy of the proton, and the fitted parameters are
 $A=0.105\textrm{ MeV}^{-1}$, $T_{th} = 1.4\textrm{ MeV}$, $\alpha = 1.328$ and
 $T_0 = 3.1\textrm{ MeV}$. The baseline
-design of the absorber is 1.0 \milli\meter~thick
+design of the absorber is 1.0 \si{\mm}~thick
 carbon-fibre-reinforced-polymer (CFRP) which contributes
-195~\kilo\electronvolt\per\cc~to the momentum resolution. The absorber also
-down shifts the conversion peak by 0.7 \mega\electronvolt. This is an issue as
+195~\si{\keV\per\cc}~to the momentum resolution. The absorber also
+down shifts the conversion peak by 0.7 \si{\MeV}. This is an issue as
 it pushes the signal closer to the DIO background region. For those reasons,
 a measurement of the rate and spectrum of proton emission after muon capture is
 required in order to optimise the CDC design.
@@ -804,41 +804,40 @@ required in order to optimise the CDC design.
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \subsection{Experimental method for proton measurement}
 \label{sub:experimental_method}
-We planned to use a low energy, narrow momentum spread available at PSI to
+We planned to use a low-energy, narrow-momentum-spread available at PSI to
 fight the aforementioned difficulties in measuring protons. The beam momentum
-is tunable from 28 to 45~\mega\electronvolt\ so that targets at different
-thickness from 25 to 100 \micro\meter\ can be studied. The $\pi$E1 beam line
-could provide about \sn{}{3} muons\per\second\ at 1\% momentum spread, and
-\sn{}{4} muons\per\second\ at 3\% momentum spread. With this tunable beam, the
-stopping distribution of the muons is well-defined. 
+is tunable from \SIrange{28}{45}{\MeV} so that targets at different
+thickness from \SIrange{25}{100}{\um} can be studied. The $\pi$E1 beam line
+could deliver \sn{}{3} muons/\si{\s} at 1\% momentum spread, and
+\sn{}{4} muons/\si{\s} at 3\% momentum spread. The muon stopping distribution
+of the muons could be well-identified using this excellent beam.  
 
-The principle of the particle identification used in the AlCap experiment is
-that for each species, the function describes the relationship between energy
-loss per unit length (dE/dx) and the particle energy E is uniquely defined.
-With a simple system of two detectors, dE/dx can be obtained by
-measuring energy deposit $\Delta$E in one detector of known thickness
-$\Delta$x, and E is the sum of energy deposit in both detector if the particle
-is fully stopped.
+Emitting charged particles from nuclear muon capture will be identified by the
+specific energy loss. The specific energy loss is calculated as energy loss
+per unit path length \sdEdx at a certain energy $E$. The quantity is uniquely
+defined for each particle species.
 
-In the AlCap, we realise the idea with a pair of silicon detectors: one thin
-detector of 65~\micron\ serves as the $\Delta$E counter, and one thick detector
-of 1500~\micron\ that can fully stop protons up to about 12~MeV. Since the
-$\Delta \textrm{d}=65$~\micron\ is known, the function relates dE/dx to
-E reduces to a function between $\Delta$E and E. Figure~\ref{fig:pid_sim} shows
-that the function of protons can be clearly distinguished from other charged
-particles in the energy range of interest. 
+The specific energy loss is measured in the AlCap using a pair of silicon
+detectors: a \SI{65}{\um}-thick detector, and a \SI{1500}{\um}-thick detector.
+Each detector is $5\times5$ \si{\cm^2} in area.
+The thinner one provides $\mathop{dE}$ information, while the sum energy
+deposition in the two gives $E$, if the particle is fully stopped. The silicon
+detectors pair could help distinguish protons from other charged particles from
+\SIrange{2.5}{12}{\MeV} as shown in \cref{fig:pid_sim}.
 \begin{figure}[htbp]
   \centering
   \includegraphics[width=0.75\textwidth]{figs/pid_sim}
-  \caption{Simulation study of PID using a pair of silicon detectors}
+  \caption{Simulation study of PID using a pair of silicon detectors. The
+    detector resolutions follow the calibration results provided by the
+    manufacturer.} 
   \label{fig:pid_sim}
 \end{figure}
 
-The AlCap uses two pairs of detector with large area, placed symmetrically with
-respect to the target provide a mean to check for muon stopping distribution.
-The absolute number of stopped muons are inferred
+Two pairs of detectors, placed symmetrically with
+respect to the target, provide a mean to check for muon stopping distribution
+inside the target. The absolute number of stopped muons is calculated
 from the number of muonic X-rays recorded by a germanium detector. For
-aluminium, the $(2p-1s)$ line is at 346 \kilo\electronvolt. The acceptances of
+aluminium, the $(2p-1s)$ line is at \SI{346.828}{\keV}. The acceptances of
 detectors will be assessed by detailed Monte Carlo study using Geant4. 
 
 % subsection experimental_method (end)
@@ -855,7 +854,7 @@ Particle Emission after Muon Capture.}\\ Protons emitted after nuclear muon
 capture in the stopping target dominate the single-hit rates in the tracking
 chambers for both the Mu2e and COMET Phase-I experiments. We plan to measure
 both the total rate and the energy spectrum to a precision of 5\% down to
-proton energies of 2.5 MeV.  
+proton energies of \SI{2.5}{\MeV}.  
 \item[WP2:] (Lynn(PNNL), Miller(BU))
 \textbf{Gamma and X-ray Emission after Muon Capture.}\\ A Ge detector will
 be used to measure X-rays from the muonic atomic cascade, in order to provide
@@ -884,7 +883,7 @@ than 1 MeV up to 10 MeV. \\
 \end{itemize}   
 
 WP1 is the most developed
-project in this program. Most of the associated apparatus has been built and
+project in this program with most of the associated apparatus has been built and
 optimized. We are ready to start this experiment in 2013, while preparing and
 completing test measurements and simulations to undertake WP2 and WP3. 
 
diff --git a/thesis/custom_macro.tex b/thesis/custom_macro.tex
index be8a058..202ffa1 100644
--- a/thesis/custom_macro.tex
+++ b/thesis/custom_macro.tex
@@ -50,6 +50,9 @@ $\mu^- \rightarrow e^- \nu_\mu \overline{\nu}_e e^+ e^-$\xspace
 
 \newcommand{\cc}{$c$\xspace}
 
+\newcommand{\dEdx}{$\dfrac{\mathop{dE}}{\mathop{dx}}$\xspace}
+\newcommand{\sdEdx}{$\sfrac{\mathop{dE}}{\mathop{dx}}$\xspace}
+
 \newcommand{\rootana}{{\ttfamily rootana}}
 \newcommand{\alcapana}{{\ttfamily alcapana}}
 \newcommand{\tpulseisland}{{\ttfamily TPulseIsland}}
diff --git a/thesis/thesis.tex b/thesis/thesis.tex
index 9aa2d7b..ac73cc3 100644
--- a/thesis/thesis.tex
+++ b/thesis/thesis.tex
@@ -32,8 +32,8 @@ for the COMET experiment}
 %\input{chapters/chap1_intro}
 %\input{chapters/chap2_mu_e_conv}
 %\input{chapters/chap3_comet}
-%\input{chapters/chap4_alcap_phys}
-%\input{chapters/chap5_alcap_setup}
+\input{chapters/chap4_alcap_phys}
+\input{chapters/chap5_alcap_setup}
 \input{chapters/chap6_analysis}
 %\input{chapters/chap7_results}