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nam
2014-10-02 16:12:17 +09:00
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151
thesis/chapters/chap5_alcap_setup.tex
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@@ -402,10 +402,11 @@ correlation between detectors would be established in the analysis stage.
At the beginning of each block, the time counter in each digitiser is reset to
ensure time alignment across all modules. The period of 110~ms was chosen to be:
{\em i} long enough compares to the time scale of several \si{\micro\second}\ of the
physics of interest, {\em ii} short enough so that there is no timer rollover
on any digitiser (a FADC runs at its maximum speed of \SI{170}{\mega\hertz} could
handle up to about \SI{1.5}{\second} with its 28-bit time counter).
{\em i} long enough compared to the time scale of several \si{\micro\second}\
of the physics of interest, {\em ii} short enough so that there is no timer
rollover on any digitiser (a FADC runs at its maximum speed of
\SI{170}{\mega\hertz} could handle up to about \SI{1.5}{\second} with its
28-bit time counter).
To ease the task of handling data, the data collecting period was divided into
short runs, each run stopped when the logger had recorded 2 GB of data.
@@ -495,8 +496,8 @@ the recorded pulse height spectrum is shown in \cref{fig:ge_eu152_spec}. The
source was placed at the target position so that the absolute efficiencies can
be calculated. The peak centroids and areas were obtained by fitting a Gaussian
peak on top of a first-order polynomial background. The only exception is the
\SI{1085.84}{\keV} line because of the interference of \SI{1089.74}{\keV},
the two were fitted with two Gaussian peaks on top of a first-order
\SI{1085.84}{\keV} line because of the interference of the \SI{1089.74}{\keV}
gamma, the two were fitted with two Gaussian peaks on top of a first-order
polynomial background.
The relation between pulse height in ADC value and energy is found to be:
@@ -527,30 +528,86 @@ a little worse at 3.1~\si{\keV}~for the annihilation photons at
\label{fig:ge_fwhm}
\end{figure}
The absolute efficiencies of the referenced points, and calculated
efficiencies at the X-ray of interest are presented in
\cref{tab:xray_eff}.
%The absolute efficiencies for the $(2p-1s)$ lines of aluminium
%(\SI{346.828}{\keV}) and silicon (\SI{400.177}{\keV})
%are presented in \cref{tab:xray_eff}.
In the process of efficiency calibration,
corrections for true coincidence summing and self-absorption were not applied.
The true coincidence summing probability is estimated to be very
small, about \num{5.4d-6}, thanks to the far geometry of the calibration. The
absorption in the source cover made of \SI{22}{\mg\per\cm^2}
polyethylene is less than \num{4d-4} for a \SI{100}{\keV} photon.
A Monte Carlo (MC) study on the acceptance of the germanium detector with two
purposes:
Following corrections for the peak areas are considered:
\begin{enumerate}
\item compare between measured and MC efficiencies: a point source made of
$^152$Eu is placed at the target position
\item estimate the uncertainty due to finite-size geometry: the source is
made of silicon with the same dimensions as those of the thick silicon
detector, namely \SI[product-units=power]{1.5 x 50 x 50}{\mm}; then the
primary vertex of $^152$Eu is generated inside the source.
\item Correction for counting loss due to finite response time of the
detector system, where two gamma rays arrive at the detector within a time
interval short compared to that response time. This correction is
significant in our germanium system because of the current pulse
information extracting method does not count the second pulse.
\item Correction of counting time loss in the reset periods of the transistor
reset preamplifier. A preamplifier of this type would reset itself after
accumulating a predetermined amount of charge. During a reset, the
preamplifier is insensitive so this can be counted as dead time.
\item True coincidence summing correction: two cascade gamma rays hit the
detector at the same time would cause loss of count under the two
respective peaks and gain under the sum energy peak.
\item Correction for self-absorption of a gamma ray by the source itself.
\end{enumerate}
The corrections for the first two mechanisms can be estimated by examining
pulse length and intervals between two consecutive pulses in the germanium
detector (\cref{fig:ge_cal_rate_pulselength}). The average pulse
length is \SI{45.7}{\um}, the average count rate obtained from the decay rate
of the interval spectrum is \SI{240}{\per\s}.
The correction factor for the finite response time of the detector system is
calculated as:
\begin{align}
k_{\textrm{finite response time}} &= e^{2\times \textrm{(pulse length)}
\times \textrm{(count rate)}}\\
&= e^{2\times 47.5\times10^{-6} \times 241} \nonumber\\
&= 1.02 \label{eqn:finite_time_response}
\end{align}
The resets of the preamplifier show up as a peak around \SI{2}{\ms},
consistent with specification of the manufacturer. Fitting the peak on top of
an exponential background gives the actual reset pulse length of
\SI{1947.34}{\us} and the number of resets during the calibration runs is
2335.0. The total time loss for resetting is hence:
$1947.34\times 10^{-6} \times 2335.0 = 4.55$ \si{\s}. That is a 0.14\% loss
for a measuring time of \SI{3245.5}{\s}. This percentage loss is insignificant
compared with the loss in \eqref{eqn:finite_time_response} and the statistical
uncertainty of peak areas so correction for amplifier resets is not applied.
\begin{figure}[htb]
\centering
\includegraphics[width=0.95\textwidth]{figs/ge_cal_rate_pulselength}
\caption{Germanium detector pulse length (left) and intervals between pulses
on that detector (right). The peak around \SI{2}{\ms} corresponds to the
resets of the preamplifier. The peak at \SI{250}{\us} is due to triggering
by the timing channel which is on the same digitiser.}
\label{fig:ge_cal_rate_pulselength}
\end{figure}
The true coincidence summing probability is estimated to be very small, about
\num{5.4d-6}, thanks to the far geometry of the calibration. The absorption in
the source cover made of \SI{22}{\mg\per\cm^2} polyethylene is less than
\num{4d-4} for a \SI{100}{\keV} photon. Therefore these two corrections are
omitted.
The absolute efficiencies of the reference gamma rays show agreement with those
obtained from a Monte Carlo (MC) study where a point source made of $^{152}$Eu
is placed at the target position (see \cref{fig:ge_eff_cal}). A comparison
between efficiencies in case of the point-like source and a finite-size
source is also done by MC simulation. As shown in \cref{fig:ge_eff_cal}, the
differences are in line with the uncertainties of the measured efficiencies.
%The dimensions of the latter are set to
%resemble the distribution of muons inside the target: Gaussian spreading
%\SI{11}{\mm} vertically, \SI{13}{\mm} horizontally, and \SI{127}{\um} in
\begin{figure}[htb]
\centering
\includegraphics[width=0.40\textwidth]{figs/ge_eff_cal}
\includegraphics[width=0.40\textwidth]{figs/ge_eff_mc_finitesize_vs_pointlike_root}
\caption{Absolute efficiency of the germanium detector, the fit was done with
7 energy points from 244~keV, the shaded area is
95\% confidence interval of the fit.}
%because it is known that the linearity between
%$ln(\textrm{E})$ and $ln(\textrm{eff})$ holds better.
\label{fig:ge_eff_cal}
\end{figure}
The absolute efficiencies of the referenced points, and calculated efficiencies
at X-rays of interest are listed in \cref{tab:xray_eff}.
\begin{table}[htb]
\begin{center}
\pgfplotstabletypeset[
@@ -601,18 +658,6 @@ purposes:
\label{tab:xray_eff}
\end{table}
\begin{figure}[htb]
\centering
\includegraphics[width=0.40\textwidth]{figs/ge_eff_cal}
\includegraphics[width=0.40\textwidth]{figs/ge_eff_mc_finitesize_vs_pointlike_root}
\caption{Absolute efficiency of the germanium detector, the fit was done with
7 energy points from 244~keV, the shaded area is
95\% confidence interval of the fit.}
%because it is known that the linearity between
%$ln(\textrm{E})$ and $ln(\textrm{eff})$ holds better.
\label{fig:ge_eff_cal}
\end{figure}
% subsection germanium_detector (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Beam tuning and muon momentum scanning}
@@ -684,12 +729,12 @@ different targets were carried out for silicon targets:
As the emitted protons deposit a significant amount of energy in the target
material, thin targets and thus excellent momentum resolution of the low energy
muon beam are critical. Aluminium targets of 50-\si{\micro\meter}\ and
100~\si{\micro\meter}\ thick were used. Although a beam with low momentum spread of
1\% is preferable, it was used for only a small portion of the run due to the
low beam rate (see \cref{fig:Rates}). The beam momentum for each target
was chosen to maximise the number of stopped muons. The collected data sets are
shown in \cref{tb:stat}.
muon beam are critical, aluminium targets of 50-\si{\micro\meter}\ and
100-\si{\micro\meter}\ thick were used. Although a beam with low momentum
spread of 1\% is preferable, it was used for only a small portion of the run
due to the low beam rate (see \cref{fig:Rates}). The beam momentum for each
target was chosen to maximise the number of stopped muons. The collected data
sets are shown in \cref{tb:stat}.
\begin{table}[btp!]
\begin{center}
@@ -865,20 +910,8 @@ update the plots to reflect real-time status of the detector system.
Some offline analysis modules has been developed during the beam time and could
provide quick feedback in confirming and guiding the decisions at the time. For
example, the X-ray spectrum analysis was done to confirm that we could observe
the muon capture process (\cref{fig:muX}), and to help in choosing optimal
momenta which maximised the number of stopped muons.
\begin{figure}[btp]
\centering
\includegraphics[width=0.7\textwidth]{figs/muX.png}
\caption{Germanium
detector spectra in the range of 300 - 450 keV with different setups: no
target, 62-\si{\micro\meter}-thick silicon target, and
100-\si{\micro\meter}-thick aluminium target. The ($2p-1s$) lines from
aluminium (346.828 keV) and silicon (400.177 keV) are clearly visible,
the double peaks at 431 and 438 keV are from the lead shield, the peak at
351~keV is a background gamma ray from $^{211}$Bi.}
\label{fig:muX}
\end{figure}
the muon capture process and to help in choosing optimal momenta which
maximised the number of stopped muons.
Although the offline analyser is still not fully developed yet, several modules
are ready. They are described in detailed in the next chapter.

6
thesis/chapters/chap6_analysis.tex
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@@ -59,7 +59,7 @@ pulses on all detector channels, and picks all pulses occur in
a time window of \SI{\pm 10}{\si{\us}} around each candidate to build
a muon event. A muon candidates is a hit on the upstream plastic scintillator
with an amplitude higher than a threshold which was chosen to reject MIPs. The
period of \SI{10}{\si{\us}} is long enough compares to the mean life time of
period of \SI{10}{\si{\us}} is long enough compared to the mean life time of
muons in the target materials
(\SI{0.758}{\si{\us}} for silicon, and \SI{0.864}{\si{\us}}
for aluminium~\cite{SuzukiMeasday.etal.1987}) so practically all of emitted
@@ -388,7 +388,7 @@ This number of X-rays needs to be corrected for following effects:
&= 1.06
\end{align}
The 2-ms-long reset pulses effectively reduce the actual measurement time
compares to other channels, so the correction factor for the effect is:
compared to other channels, so the correction factor for the effect is:
\begin{align}
k_{\textrm{reset pulse}} &= \frac{\textrm{(measurement time)}}
{\textrm{(measurement time)}
@@ -830,7 +830,7 @@ The uncertainty of the emission rate could come from several sources:
collimator. In the worst case when the muon beam is flatly distributed,
that displacement could change the acceptance of the silicon detectors by
12\%. Although no measurement was done to determine the efficiency of the
silicon detectors, it would have small effect compare to other factors.
silicon detectors, it would have small effect compared to other factors.
\end{enumerate}
The combined uncertainty from known sources above therefore could be as large