\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)