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+\chapter{Discussions}
+\label{cha:discussions}
+
+\section{Thick aluminium target measurement}
+\label{sub:active_target_measurement}
+With a thick and active silicon target, I have tried to reproduce an existing
+result from Sobottka and Wills~\cite{SobottkaWills.1968}. This is important in
+giving confidence in our experimental method. The idea is the same as that of
+the old measurement, where muons were stopped inside a bulk active target and
+the capture products were measured. Due to the limitation of the
+currently available analysis tool, a direct comparison with the result of
+Sobottka and Wills is not practical at the moment.
+
+But a partial comparison is available for a part of the spectrum from 8 to
+10~MeV, where my result of $(1.22 \pm 0.19) \times 10^{-2} $ is consistent with
+the derived value $(1.28\pm0.19)\times10^{-2}$ from the paper of Sobottka and
+Wills. The agreement was partly because of large error bars in both results.
+In my part, the largest error came from the uncertainty on choosing the
+integration window. This can be solved with a more sophisticated pulse
+finding/calculating algorithm so that the contribution of muons in the energy
+spectrum can be  eliminated by imposing a cut in pulse timing. The
+under-testing pulse template fitting module could do this job soon.
+
+The range of 8--10~MeV was chosen to be large enough so that the uncertainty of
+integration window would not to be too great; and at the same time be small
+enough so the protons (and other heavier charged particles) would not escape
+the active target. This range is also more convenient for calculating the
+partial rate from the old paper of Sobottka and Wills.
+
+% section protons_following_muon_capture_on_silicon (end)
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\section{Thin silicon target measurement}
+\label{sub:thin_and_passive_target_measurement}
+The charged particles in the low energy region of 2.5--8~MeV were measured by
+dE/dx method. The particle identification was good in lower energy part, but
+losing its resolution power as energy increases. The current set up could do
+the PID up to about 8~MeV for protons. This energy range is exactly the
+relevant range to the COMET experiment (Figure~\ref{fig:proton_impact_CDC}). 
+
+In that useful energy range, the analysis showed a good separation of protons
+from other heavy charged particles. The contribution of protons in the total
+charged particles is 87\%. This is the high limit only since the heavier
+particles at this energy range are most likely to stopped in the thin
+detectors. More statistic would be needed to estimate the contributions from
+other particles.
+
+The effective emission rate of protons per muon capture in this measurement is
+4.20\%, with a large uncertainty contribution comes from limitation of the
+timing determination. The spectral integral in the region 2.5--8~MeV on
+Figure~\ref{fig:sobottka_spec} is about 70\% of the spectrum from 1.4 to
+26~\MeV, and corresponds to an emission rate of about 10\% per muon capture.
+The two figures are not in disagreement.
+
+In order to have a better comparison, a correction or unfolding  for energy
+loss and more MC simulation study are needed. I am on progress of these study.
+
+% subsection thin_and_passive_target_measurement (end)
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Aluminium target measurement}
+\label{sec:aluminium_target_measurement}
+The proton emission rate was derived as 2.37\%, but the problem on the SiL1-1
+channel was not solved yet. One possible cause is the muons captured on other
+lighter material inside the chamber. More investigation will be made on this
+matter.
+
+The rate of 2.37\% on aluminium appears to be smaller on that of silicon but
+the two results are both effective rates, modified by energy loss inside the
+target. Unfolding and MC study for the correction are ongoing. 
+% section aluminium_target_measurement (end)
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% chapter discussions (end)
+
+