From 36ae84607f55cf06763fec4c122672e9de42b366 Mon Sep 17 00:00:00 2001 From: nam Date: Fri, 12 Sep 2014 19:17:32 +0900 Subject: [PATCH] prog saved --- thesis/Makefile | 2 +- thesis/chapters/chap5_alcap_setup.tex | 249 +++++++++++++++++ thesis/chapters/chap6_analysis.tex | 373 +++++++------------------- thesis/mythesis.sty | 5 +- thesis/thesis.tex | 6 +- 5 files changed, 357 insertions(+), 278 deletions(-) diff --git a/thesis/Makefile b/thesis/Makefile index ce15a60..9bd3694 100644 --- a/thesis/Makefile +++ b/thesis/Makefile @@ -5,7 +5,7 @@ TARGET= $(DOCNAME).pdf default: $(TARGET) -$(TARGET): $(INPUT) Makefile chapters/*.tex custom_macro.tex mythesis.sty +$(TARGET): $(INPUT) Makefile chapters/*.tex custom_macro.tex mythesis.sty raw/* @rm -f $(DOCNAME).{aux,toc,lof,lot} pdflatex $< && bibtex $(DOCNAME) && pdflatex $< && pdflatex $< diff --git a/thesis/chapters/chap5_alcap_setup.tex b/thesis/chapters/chap5_alcap_setup.tex index 5672daa..481bb34 100644 --- a/thesis/chapters/chap5_alcap_setup.tex +++ b/thesis/chapters/chap5_alcap_setup.tex @@ -289,6 +289,7 @@ carried out. % subsection plastic_scintillators (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Front-end electronics and data acquisition system} The front-end electronics of the AlCap experiment was simple since we employed a trigger-less read out system with waveform digitisers and flash ADCs @@ -413,6 +414,254 @@ automatically starts a new run with the same parameters after about 6 seconds. The short period of each run also allows the detection, and helps to reduce the influence of effects such as electronics drifting, temperature fluctuation. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Detector calibration} +\label{sec:detector_calibration} +The calibration was done mainly for the silicon and germanium detectors +because they would provide energy information. The plastic scintillators were +only checked by oscilloscopes to make sure that the minimum ionisation +particles (MIPs) could be observed. The upstream plastic scintillation +counters and wire chamber, as mentioned, were well-tuned by the MuSun group. + +\subsection{Silicon detector} +\label{sub:silicon_detector} +The energy calibration for the silicon detectors were done routinely during the +run, by: +\begin{itemize} + \item a \SI{79.5}{\becquerel} $^{241}\textrm{Am}$ alpha source. The most + prominent alpha particles have energies of \SI{5.484}{\si{\MeV}} (85.2\%) + and \SI{5.442}{\si{\MeV}} (12.5\%). The alpha particles from the source + would lose about \SI{66}{\kilo\eV} in the \SI{0.5}{\um}-thick dead layer, + and the peak would appear at \SI{5418}{\kilo\eV} (\cref{fig:toyMC_alpha}); + + \item and a tail pulse generator, A tail pulse with amplitude of + \SI{66}{\milli\volt}~was used to simulate the response of the silicon + detectors' preamplifiers to a particle with \SI{1}{\MeV} energy deposition; + + \item During data taking period, electrons in the beam were were also used + for energy calibration of thick silicon detectors where energy deposition + is large enough. The muons at different momenta provided another mean of + calibration in the beam tuning period. +\end{itemize} + +\begin{figure}[htb] + \centering + \includegraphics[width=0.6\textwidth]{figs/toyMC_alpha} + \caption{Energy loss of the alpha particles after a dead layer of + \SI{0.5}{\um}.} + \label{fig:toyMC_alpha} +\end{figure} + +The calibration coefficients for the silicon channels are listed in +\cref{tab:cal_coeff}. + +\begin{table} + \begin{center} + \pgfplotstabletypeset[ + % separator + col sep=comma, + % columns displayed + display columns/0/.style={column name = \textbf{Detector}, string type, + column type=l}, + display columns/1/.style={column name = \textbf{Slope}, column type=c, + dec sep align}, + display columns/2/.style={column name = \textbf{Offset}, column type=r, + dec sep align}, + % format the line breaks + every head row/.style={ + before row={\toprule}, + after row={\midrule}, + columns/Detector/.style={column type=c}, + columns/Slope/.style={column type=c}, + columns/Offset/.style={column type=c} + }, + every last row/.style={after row=\bottomrule}, + ]{raw/si_cal_effs.csv} + \caption{Calibration coefficients of the silicon detector channels} + \label{tab:cal_coeff} + \end{center} +\end{table} +% subsection silicon_detector (end) +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Germanium detector} +\label{sub:germanium_detector} +The germanium detector was calibrated using a $^{152}\textrm{Eu}$ +source +\footnote{Energies and intensities of gamma rays are taken from the + X-ray and Gamma-ray Decay Data Standards for Detector Calibration and Other + Applications, which is published by IAEA at \\ + \url{https://www-nds.iaea.org/xgamma_standards/}}, +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 +polynomial background. + +The relation between pulse height in ADC value and energy is found to be: +\begin{equation} + \textrm{ E [keV]} = 0.1219 \times \textrm{ADC} + 1.1621 +\end{equation} +The energy resolution (full width at half maximum - FWHM) was better than +2.6~\si{\keV}\ for all the $^{152}\textrm{Eu}$ peaks. It was +a little worse at 3.1~\si{\keV}~for the annihilation photons at +511.0~\si{\keV}. + +\begin{figure}[htb] + \centering + \includegraphics[width=0.70\textwidth]{figs/ge_eu152_spec} + \caption{Energy spectrum of the $\rm^{152}\textrm{Eu}$ calibration source + recorded by the germanium detector. The most prominent peaks of + $^{152}\textrm{Eu}$ along with their energies are + annotated in red; the 1460.82 \si{\keV}~line is background from + $^{40}\textrm{K}$; and the annihilation 511.0~\si{\keV}~photons + come both from the source and the surrounding environment.} + \label{fig:ge_eu152_spec} +\end{figure} + +\begin{figure}[htb] + \centering + \includegraphics[width=0.89\textwidth]{figs/ge_ecal_fwhm} + \caption{Germanium energy calibration and resolution.} + \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: +\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. +\end{enumerate} + +\begin{table}[htb] + \begin{center} + \pgfplotstabletypeset[ + % separator + col sep=comma, + % columns displayed + % column type={S} means leave formatting to siunitx + display columns/0/.style={column name = \textbf{Photons (\si{\keV})}, + string type, + column type={S[table-format=4.3, table-alignment=center]}}, + display columns/1/.style={column name = \textbf{Efficiency}, + string type, + column type={S[parse-numbers = true, + round-precision=3, + round-mode=figures, + fixed-exponent=-4, + scientific-notation=fixed, + table-format=1.2e-1, + %table-omit-exponent, + ]}}, + display columns/2/.style={column name = \textbf{Uncertainty}, + string type, + column type={S[parse-numbers = true, + round-precision=3, + round-mode=figures, + fixed-exponent=-5, + scientific-notation=fixed, + table-format=1.3e-1, + %table-omit-exponent, + ]}}, + % format the line breaks + every head row/.style={ + before row={\toprule}, + after row={ + %\textbf{\si{\keV}} & \textbf{\num{E-4}} & \textbf{\num{E-4}}\\ + \midrule}, + columns/0/.style={column type=r}, + columns/1/.style={column type=c}, + columns/2/.style={column type=c} + }, + every last row/.style={after row=\bottomrule}, + every nth row={8}{before row={\midrule}}, + ]{raw/ge_eff.csv} + \end{center} + \caption{Absolute efficiencies of the germanium detector in case of + a point-like source placed at the centre of the target (upper half), and + the calculated efficiencies for the X-rays of interest (lower half).} + \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} +%\label{sub:muon_momentum_scanning} +%Before taking any data, we carried out the muon momentum scanning to understand +%the muon beam, as well as calibrate the detector system. The nominal muon +%momentum used in the Run 2013 had been tuned to 28~MeV\cc\ before the run. By +%changing simultaneously the strength of the key magnet elements in the $\pi$E1 +%beam line with the same factor, the muon beam momentum would be scaled with the +%same factor. + +%The first study was on the range of muons in an active silicon target. The SiL2 +%detector was placed perpendicular to the nominal beam path, after an oval +%collimator. The beam momentum scaling factor was scanned from 1.10 to 1.60, +%muon momenta and energies in the measured points are listed in +%\cref{tab:mu_scales}. +%\begin{table}[htbp] + %\begin{center} + %\begin{tabular}{c c c c} + %\toprule + %\textbf{Scaling} & \textbf{Momentum} & \textbf{Kinetic energy} + %& \textbf{Momentum spread}\\ + %\textbf{factor} & \textbf{(MeV\per\cc)} & \textbf{(MeV)} + %& \textbf{(MeV\per\cc, 3\% FWHM)}\\ + %\midrule + %1.03 & 28.84 & 3.87& 0.87\\ + %1.05 & 29.40 & 4.01& 0.88\\ + %1.06 & 29.68 & 4.09& 0.89\\ + %1.07 & 29.96 & 4.17& 0.90\\ + %1.10 & 30.80 & 4.40& 0.92\\ + %1.15 & 32.20 & 4.80& 0.97\\ + %1.20 & 33.60 & 5.21& 1.01\\ + %1.30 & 36.40 & 6.09& 1.09\\ + %1.40 & 39.20 & 7.04& 1.18\\ + %1.43 & 40.04 & 7.33& 1.20\\ + %1.45 & 40.60 & 7.53& 1.22\\ + %1.47 & 41.16 & 7.73& 1.23\\ + %1.50 & 42.00 & 8.04& 1.26\\ + %\bottomrule + %\end{tabular} + %\end{center} + %\caption{Muon beam scaling factors, energies and momenta.} + %\label{tab:mu_scales} +%\end{table} + +% subsection muon_momentum_scanning (end) +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% section detector_calibration (end) +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Data sets and statistics} \label{sec:data_sets} diff --git a/thesis/chapters/chap6_analysis.tex b/thesis/chapters/chap6_analysis.tex index cc50dfe..6585976 100644 --- a/thesis/chapters/chap6_analysis.tex +++ b/thesis/chapters/chap6_analysis.tex @@ -37,9 +37,8 @@ for pulse information calculation is in use. The module looks for the sample that has the maximal deviation from the baseline, takes the deviation as pulse amplitude and the time stamp of the sample as pulse time. The procedure is -illustrated on \cref{fig:tap_maxbin_algo}. This module could not detect -pile up or double pulses in one \tpulseisland{} in -\cref{fig:tap_maxbin_bad}. +illustrated on \cref{fig:tap_maxbin_algo}. This module could not account for +pile-up or double pulses in one \tpulseisland{} in \cref{fig:tap_maxbin_bad}. \begin{figure}[htb] \centering \includegraphics[width=0.85\textwidth]{figs/tap_maxbin_algo} @@ -57,12 +56,12 @@ pile up or double pulses in one \tpulseisland{} in The TSimpleMuonEvent first picks a muon candidate, then loops through all pulses on all detector channels, and picks all pulses occur in -a time window of \SI{\pm 10}{\si{\micro\second}} around each candidate to build +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 minimum -ionising particles (MIPs). The period of \SI{10}{\si{\micro\second}} is long -enough compares to the mean life time of muons in the target materials -(\SI{0.758}{\si{\micro\second}} for silicon, and \SI{0.864}{\si{\micro\second}} +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 +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 charged particles would be recorded in this time window. %\begin{figure}[htb] @@ -73,13 +72,13 @@ charged particles would be recorded in this time window. %\end{figure} A pile-up protection mechanism is employed to reject multiple muons events: if -there exists another muon hit in less than \SI{15}{\si{\micro\second}} from the +there exists another muon hit in less than \SI{15}{\si{\us}} from the candidate then both the candidate and the other muon are discarded. This pile-up protection would cut out less than 11\% total number of events because the beam rate was generally less than \SI{8}{\kilo\hertz}. %In runs with active silicon targets, another requirement is applied for the -%candidate: a prompt hit on the target in $\pm 200$ \si{\nano\second}\ around the +%candidate: a prompt hit on the target in $\pm 200$ \si{\ns}\ around the %time of the $\mu$Sc pulse. The number comes from the observation of the %time correlation between hits on the target and the $\mu$Sc %(\cref{fig:tme_sir_prompt_rational}). @@ -112,193 +111,13 @@ shown in \cref{fig:lldq}. \end{figure} % section analysis_modules (end) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\section{Detector calibration} -\label{sec:detector_calibration} - -\subsection{Silicon detector} -\label{sub:silicon_detector} -The energy calibration for the silicon detectors were done routinely during the -run, mainly by an -$^{241}\textrm{Am}$ alpha source and a tail pulse generator. The source emits -79.5 $\alpha$\si{\per\second} in a \SI{2\pi}{\steradian} solid angle. The most -prominent alpha particles have energies of \SI{5.484}{\si{\mega\electronvolt}} -(85.2\%) and \SI{5.442}{\si{\mega\electronvolt}} (12.5\%). A tail pulse with -amplitude of -\SI{66}{\milli\volt}~was used to simulate the response of the silicon detectors' -preamplifiers to a particle with \SI{1}{\si{\mega\electronvolt}} energy deposition. - -During data taking period, electrons in the beam were were also used for energy -calibration of thick silicon detectors where energy deposition is large enough. -The muons at different momenta provided another mean of calibration in the beam -tuning period. - -The alpha particles from the source would deposit -about 66~keV in the \SI{0.5}{\micro\meter}-thick dead layer, and the peak would -appear at 5418~keV (\cref{fig:toyMC_alpha}). -\begin{figure}[htb] - \centering - \includegraphics[width=0.6\textwidth]{figs/toyMC_alpha} - \caption{Energy loss of the alpha particles after a dead layer of - 0.5~\si{\micro\meter}.} - \label{fig:toyMC_alpha} -\end{figure} - -The calibration coefficients for the silicon channels are listed in -\cref{tab:cal_coeff}. -\begin{table}[htb] - \begin{center} - \begin{tabular}{l c r} - \toprule - \textbf{Detector} & \textbf{Slope} & \textbf{Offset}\\ - \midrule - SiL-2 & 7.86 & 14.14\\ - SiR-2 & 7.96 & 22.98\\ - \midrule - SiL1-1 & 2.61 & 37.34\\ - SiL1-2 & 2.54 & -20.78\\ - SiL1-3 & 2.65 & 67.75\\ - SiL1-4 & 2.54 & -18.45\\ - \midrule - SiR1-1 & 2.53 & 28.69\\ - SiR1-2 & 2.62 & 47.10\\ - SiR1-3 & 2.49 & 6.32\\ - SiR1-4 & 2.53 & 34.81\\ - \bottomrule - \end{tabular} - \end{center} - \caption{Calibration coefficients of the silicon detector channels} - \label{tab:cal_coeff} -\end{table} -% subsection silicon_detector (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{Germanium detector} -\label{sub:germanium_detector} -The germanium detector was calibrated using a $^{152}\textrm{Eu}$ -source\footnote{Energies and intensities of gamma rays are taken from the - X-ray and Gamma-ray Decay Data Standards for Detector Calibration and Other - Applications, which is published by IAEA at \\ - \url{https://www-nds.iaea.org/xgamma_standards/}}, 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 calibrated. The relation between pulse height in ADC count and energy is -found to be: -\begin{equation} - \textrm{ E [keV]} = 0.1219 \times \textrm{ADC} + 1.1621 -\end{equation} -The energy resolution (full width at half maximum) was better than -2.6~\si{\kilo\electronvolt}\ for all the $^{152}\textrm{Eu}$ peaks. It was a little -worse at 3.1~\si{\kilo\electronvolt}~for the annihilation photons at -511.0~\si{\kilo\electronvolt}. - -The absolute efficiencies for the $(2p-1s)$ lines of aluminium -(346.828~\si{\kilo\electronvolt}) and silicon (400.177~\si{\kilo\electronvolt}) 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 \sn{5.4}{-6}, thanks to the far geometry of the calibration. The -absorption in the source cover made of 22~\si{\milli\gram\per\si{\centi\meter}^2} -polyethylene is less than \sn{4}{-4} for a 100~\si{\kilo\electronvolt}\ photon. - -\begin{table}[htb] - \begin{center} - \begin{tabular}{c c c} - \toprule - \textbf{X-ray} & \textbf{Efficiency} & \textbf{Uncertainty}\\ - \midrule - 346.828 & $5.12 \times 10^{-4}$ & $0.14\times 10^{-4}$\\ - 400.177 & $4.54 \times 10^{-4}$ & $0.11\times 10^{-4}$\\ - \bottomrule - \end{tabular} - \end{center} - \caption{Calculated efficiencies at X-rays of interest} - \label{tab:xray_eff} -\end{table} - -\begin{figure}[htb] - \centering - \includegraphics[width=0.70\textwidth]{figs/ge_eu152_spec} - \caption{Energy spectrum of the $\rm^{152}\textrm{Eu}$ calibration source - recorded by the germanium detector. The most prominent peaks of - $^{152}\textrm{Eu}$ along with their energies are - annotated in red; the 1460.82 \si{\kilo\electronvolt}~line is background from - $^{40}\textrm{K}$; and the annihilation 511.0~\si{\kilo\electronvolt}~photons - come both from the source and the surrounding environment.} - \label{fig:ge_eu152_spec} -\end{figure} - -\begin{figure}[htb] - \centering - \includegraphics[width=0.89\textwidth]{figs/ge_ecal_fwhm} - \caption{Germanium energy calibration and resolution.} - \label{fig:ge_fwhm} -\end{figure} - -\begin{figure}[htb] - \centering - \includegraphics[width=0.80\textwidth]{figs/ge_ecal_eff} - \caption{Absolute efficiency of the germanium detector, the fit was done with - 7 energy points from 244~keV because it is known that the linearity between - $ln(\textrm{E})$ and $ln(\textrm{eff})$ holds better. The shaded area is - 95\% confidence interval of the fit.} - \label{fig:ge_eff} -\end{figure} - -% subsection germanium_detector (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%\subsection{Beam tuning and muon momentum scanning} -%\label{sub:muon_momentum_scanning} -%Before taking any data, we carried out the muon momentum scanning to understand -%the muon beam, as well as calibrate the detector system. The nominal muon -%momentum used in the Run 2013 had been tuned to 28~MeV\cc\ before the run. By -%changing simultaneously the strength of the key magnet elements in the $\pi$E1 -%beam line with the same factor, the muon beam momentum would be scaled with the -%same factor. - -%The first study was on the range of muons in an active silicon target. The SiL2 -%detector was placed perpendicular to the nominal beam path, after an oval -%collimator. The beam momentum scaling factor was scanned from 1.10 to 1.60, -%muon momenta and energies in the measured points are listed in -%\cref{tab:mu_scales}. -%\begin{table}[htbp] - %\begin{center} - %\begin{tabular}{c c c c} - %\toprule - %\textbf{Scaling} & \textbf{Momentum} & \textbf{Kinetic energy} - %& \textbf{Momentum spread}\\ - %\textbf{factor} & \textbf{(MeV\per\cc)} & \textbf{(MeV)} - %& \textbf{(MeV\per\cc, 3\% FWHM)}\\ - %\midrule - %1.03 & 28.84 & 3.87& 0.87\\ - %1.05 & 29.40 & 4.01& 0.88\\ - %1.06 & 29.68 & 4.09& 0.89\\ - %1.07 & 29.96 & 4.17& 0.90\\ - %1.10 & 30.80 & 4.40& 0.92\\ - %1.15 & 32.20 & 4.80& 0.97\\ - %1.20 & 33.60 & 5.21& 1.01\\ - %1.30 & 36.40 & 6.09& 1.09\\ - %1.40 & 39.20 & 7.04& 1.18\\ - %1.43 & 40.04 & 7.33& 1.20\\ - %1.45 & 40.60 & 7.53& 1.22\\ - %1.47 & 41.16 & 7.73& 1.23\\ - %1.50 & 42.00 & 8.04& 1.26\\ - %\bottomrule - %\end{tabular} - %\end{center} - %\caption{Muon beam scaling factors, energies and momenta.} - %\label{tab:mu_scales} -%\end{table} - -% subsection muon_momentum_scanning (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% section detector_calibration (end) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Charged particles following muon capture on a thick silicon target} \label{sec:charged_particles_from_muon_capture_on_silicon_thick_silicon} -This analysis was done on a subset of the active target runs 2119 -- 2140 -because of the problem of wrong clock frequency found in the data quality -checking shown in \cref{fig:lldq}. The data set contains \sn{6.43}{7} -muon events. -%64293720 +This analysis was done on a subset of the active target runs +\numrange{2119}{2140} because of the problem of wrong clock frequency found in +the data quality checking shown in \cref{fig:lldq}. The data set contains +%\num[fixed-exponent=2, scientific-notation = fixed]{6.4293720E7} muon events. +\num{6.43E7} muon events. Firstly, the number of charged particles emitted after nuclear muon capture on the active target is calculated. This number then is normalised to the number @@ -309,15 +128,15 @@ compared with that from the literature. \label{sub:event_selection} Because of the active target, a stopped muon would cause two coincident hits on the muon counter and the target. The energy of the muon hit on the active -target is also well-defined as a narrow momentum spread beam was used. The +target is also well-defined as the narrow-momentum-spread beam was used. The correlation between the energy and timing of all the hits on the active target is shown in \cref{fig:sir2f_Et_corr}. The most intense spot at zero time and about 5 MeV energy corresponds to stopped muons in the thick target. The band below 1 MeV is due to electrons, either in the beam or from muon decay in orbits, or emitted during the cascading of muon to the muonic 1S state. The valley between time zero and 1200~ns shows the minimum distance in time between -two pulses. It is the limitation of the current pulse parameter extraction -method where no pile up or double pulses is accounted for. +two pulses. It is the mentioned limitation of the current pulse parameter +extraction method where no pile up or double pulses is accounted for. \begin{figure}[htb] \centering @@ -352,12 +171,12 @@ From the energy-timing correlation above, the cuts to select stopped muons are: and the first hit on the silicon active target is in coincidence with that muon counter hit: \begin{equation} - \lvert t_{\textrm{target}} - t_{\mu\textrm{ counter}}\rvert<50\textrm{ ns} + \lvert t_{\textrm{target}} - t_{\mu\textrm{ counter}}\rvert \le \SI{50}{\ns} \label{eqn:sir2_prompt_cut} \end{equation} \item the first hit on the target has energy of that of the muons: \begin{equation} - 3.4 \textrm{ MeV}