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thesis/chapters/chap4_alcap_phys.tex

@@ -540,15 +540,16 @@ Wyttenbach et al.~\cite{WyttenbachBaertschi.etal.1978} studied $(\mu^-,\nu p)$,
 $(\mu^-,\nu pn)$, $(\mu^-,\nu p2n)$, $(\mu^-,\nu p3n)$ and $(\mu^-,\nu\alpha)$
 in a wide range of 18 elements from sodium to bismuth.Their results plotted
 against the Coulomb barrier for the outgoing protons are given in
-\cref{fig:wyttenbach_rate_1p} and \cref{fig:wyttenbach_rate_23p}. The
-classical Coulomb barrier $V$ they used are given by:
+\cref{fig:wyttenbach_rate_1p}. 
+%and \cref{fig:wyttenbach_rate_23p}.
+The classical Coulomb barrier $V$ they used are given by:
 \begin{equation}
   V = \frac{zZe^2}{r_0A^{\frac{1}{3}} + \rho},
   \label{eqn:classical_coulomb_barrier}
 \end{equation}
 where $z$ and $Z$ are the charges of the outgoing particle and of the residual
-nucleus respectively, $r_0 = 1.35 \textrm{ fm}$, and $\rho = 0 \textrm{ fm}$ for
-protons were taken.
+nucleus respectively, $e^2 = 1.44 \si{\MeV}$, $r_0 = 1.35 \textrm{ fm}$, and
+$\rho = 0 \textrm{ fm}$ for protons were taken.
 \begin{figure}[htb]
   \centering
     \includegraphics[width=0.48\textwidth]{figs/wyttenbach_rate_1p}
@@ -805,15 +806,14 @@ not of concern because they have lower kinetic energy compared with protons and
 higher stopping power, thus are harder to escape the muon stopping target.
 \begin{figure}[htb]
   \centering
-    \includegraphics[width=0.85\textwidth]{figs/proton_impact_CDC}
-  \caption{Momentum kinetic energy relation of protons, deuterons and alphas
-  below 10\si{\MeV}. Shaded area is the acceptance of the COMET
-  Phase-I's CDC. Protons with energies in higher than \SI{2.5}{\MeV} are in the
-  acceptance of the CDC. Deuterons and alphas at low energies should be stopped
-  inside the muon stopping target.}
+  \includegraphics[width=0.85\textwidth]{figs/alcap_proton_vs_acceptance}
+  \caption{Momentum - kinetic energy relation of protons, deuterons and alphas
+    at low energy region below 20\si{\MeV}. Charged particles in the shaded
+    area could reach the COMET Phase-I's CDC, for protons that corresponds
+    kinetic energies higher than \SI{2.5}{\MeV}. Deuterons and alphas at low
+    energies should be stopped inside the muon stopping target.}
   \label{fig:proton_impact_CDC}
 \end{figure}
-%%TODO replace a figure without upper limit
 
 The COMET plans to introduce a thin, low-$Z$ proton absorber in between the
 target and the CDC to reduce proton hit rate. The absorber will be effective
@@ -846,7 +846,7 @@ cut-off value of $T_{th}$, its rising edge is governed by the parameter
 $\alpha$. The exponential decay component dominates at higher energy.
 
 The baseline design of the proton absorber for the COMET Phase-I based on
-above assumptions is a 1-\si{\mm}-thick CFRP layer as has been described in
+above assumptions is a 0.5-\si{\mm}-thick CFRP layer as has been described in
 \cref{ssub:hit_rate_on_the_cdc}.  The hit rate estimation is
 conservative and the contribution of the absorber to the momentum resolution
 is not negligible, further optimisation is desirable. Therefore a measurement