227 lines
8.7 KiB
TeX
227 lines
8.7 KiB
TeX
\documentclass[11pt]{article}
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\usepackage{mhchem}
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\usepackage{booktabs}
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\usepackage{multirow}
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\usepackage{textcomp}
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\usepackage{epsfig}
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\usepackage{hyperref}
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\usepackage[noabbrev, capitalize]{cleveref} % hyperref must be loaded first
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\usepackage[
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detect-weight=true,
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per=slash,
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detect-family=true,
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separate-uncertainty=true]{siunitx}
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% \usepackage{listings}
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\usepackage{xcolor}
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\usepackage{upquote}
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\usepackage{minted}
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\usemintedstyle{perldoc}
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\usepackage{mdframed}
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\definecolor{greybg}{rgb}{0.25,0.25,0.25}
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\definecolor{yellowbg}{rgb}{0.91, 0.84, 0.42}
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\definecolor{bananamania}{rgb}{0.98, 0.91, 0.71}
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\mdfsetup{%
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middlelinecolor=red,
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middlelinewidth=2pt,
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backgroundcolor=yellow!40,
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roundcorner=20pt}
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% \DeclareSIUnit\eVperc{\eV\per\clight}
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% \DeclareSIUnit\clight{\text{\ensuremath{c}}}
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\begin{document}
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\title{Hit rate estimation for STM detectors}
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\author{Nam H. Tran \\ Boston University}
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\date{\today}
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\maketitle
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\begin{abstract}
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This report presents estimated hit rate on STM detectors with the updated
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geometry in Offline version TODO.
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\end{abstract}
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\section{Overview}
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\label{sec:overview}
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In order to measure the eponymous rate of the Mu2e experiment, the number of
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stopped muons needs to be known to about \SI{10}{\percent}. The most promising
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schemes have involved photon detectors far downstream of the Muon Beam Stop
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measuring emissions from the Stopping Target (ST) at different times with
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respect to each pulse of muons stopping in the target. There are three
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categories we explore here for this stopping-target monitor (STM):
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\begin{itemize}
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\item Prompt: X-rays emitted when the muon comes to rest in the ST and is
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captured into atomic orbit (atomic capture, sometimes referred to as “muon
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stop” in this text). These X-rays are emitted essentially O(ps) with the
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atomic capture time.
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\item Semiprompt: $\gamma$-rays emitted upon nuclear capture (sometimes
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referred to simply as ``capture'' in this text) of the muon after stop.
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These exhibit timing characteristics of the muonic lifetime ($\tau
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= \SI{864}{\ns}$).
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\item Delayed: $\gamma$-rays from activated daughters resulting from muon
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nuclear capture in the ST.
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\end{itemize}
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The baseline design of the STM has been described by Miller et
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al~\cite{Miller2016}, the estimated hit rate on STM detector was about
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\SI{1.1}{\kHz} in the time window \SIrange{200}{1695}{\ns} from arrival time of
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a proton bunch. But this design would cause a high hit rate on the Cosmic
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Ray Veto (CRV) system, therefore changes have been made in the Offline version
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v6\textunderscore 0\textunderscore 2 by the CRV team to reduce the CRV hit
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rate. The goal of this study is to re-estimate hit rates on STM detectors in
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this new geometry.
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The actual changes relevant to the STM are:
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\begin{itemize}
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\item \SI{10}{\mm} polyethylene liner added to CRV shielding,
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\item field-of-view (FOV) collimator absorber thickness reduced to
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\SI{10}{\mm} (from \SI{20}{\mm}).
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\end{itemize}
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\section{Simulation details}
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\label{sec:simulation_details}
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The study was done using Mu2e Offline version v6\textunderscore
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0\textunderscore 2 (released on Oct 16,
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2016), hashtag \texttt{3d1e9154d7}. The simulation starts from the entrance of
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TS5 (see \cref{fig:stm_geo_all}), taking \texttt{cd3-beam-g4s2-mubeam.0728a}
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dataset as input. The dataset contains 5098 files, each corresponds to
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\num{1e6} proton-on-target (POT). The dataset were reused 16 times with
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different random seeds, where \SI{97}{\percent} of runs succeeded, equivalent
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to \num{8e11} POTs.
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\begin{figure}[htbp]
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\centering
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\includegraphics[width=1.0\textwidth]{figs/stm_geo_all}
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\caption{Simulation geometry showing the DS region on the left, sweeper magnet,
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FOV collimator, spot-size collimator, and the STM detectors on the right.
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Particles saved in the input files are shoot from the TS5 (orange circle),
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and transported to the STM region.}
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\label{fig:stm_geo_all}
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\end{figure}
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There were 8 virtual detectors (VD) in STM region enabled in this study, their
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identification numbers (\texttt{vdid}), locations, and abbreviation names
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(appear in the simulation output) are listed in \cref{tab:vds_list}.
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Information recorded by the VDs includes: particle type (\texttt{pdgid}),
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global and local coordinates, time, kinetic energy, and parent particle type.
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Only particles considered important to the STM, namely electrons,
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positrons, negative and positive muons, neutrons and photons, were written to
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the output file.
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\begin{table}[htbp]
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\centering
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\caption{List of virtual detectors read out in this study}
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\label{tab:vds_list}
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\begin{tabular}{@{}ccll@{}}
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\toprule
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&VDID & Location & Abbreviation \\
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\midrule
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1 & 81 & Exit of neutron shield of the DS & DSNeutronShieldExit \\
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2 & 86 & Upstream of the STM system & STM\textunderscore UpStr \\
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3 & 87 & Downstream of the sweeper magnet & STM\textunderscore MagDnStr \\
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4 & 101 & Upstream of the spot-size collimator & STM\textunderscore SpotSizeCollUpStr \\
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5 & 88 & Downstream of the spot-size collimator& STM\textunderscore CollDnStr \\
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6 & 89 & Upstream of the STM detector 1 & STM\textunderscore Det1UpStr \\
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7 & 90 & Upstream of the STM detector 2 & STM\textunderscore Det2UpStr \\
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8 & 100 & Downstream of the FOV collimator & STM\textunderscore FieldOfViewCollDnStr \\
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\bottomrule
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\end{tabular}
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\end{table}
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\section{Simulation and analysis code}
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\label{sec:simulation_and_analysis_code}
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The simulation and analysis code are located at:
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\url{/mu2e/app/users/namtran/STM_study_201611}.
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% \lstinputlisting[language=bash,frame=single]{listings/code_dir_tree.sh}
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\begin{mdframed}
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\inputminted{bash}{listings/code_dir_tree.sh}
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\end{mdframed}
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\texttt{step00} contains configuration files for this simulation and a script to
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submit all 5098 jobs (correspond to number of input files) to the FermiGrid.
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It took about 14 hours to complete a job in average.
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The \texttt{analysis} folder contains a script
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(\texttt{run\textunderscore statistics.sh}) which checks if a job has finished
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successfully, and makes a list of such runs.
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There is a simple analysis code (\texttt{main.cc}) to read the VD records and
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make plots.
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\section{Results}
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\label{sec:results}
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\subsection{STM detector spectra}
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\label{sub:stm_detector_spectra}
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Energy spectrum of particles hitting STM detectors are presented in
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\cref{fig:stm_det_ke}. There were not many hits, and only the annihilation
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peak stands out. Most of the particles are photons as shown in
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\cref{fig:stm_det_ptype}.
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\begin{figure}[htbp]
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\centering
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\includegraphics[width=0.7\textwidth]{figs/ke_det1UpStr}
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\includegraphics[width=0.7\textwidth]{figs/ke_det2UpStr}
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\caption{Kinetic energy of particles hitting STM detectors 1 (top), and
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2 (bottom).}
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\label{fig:stm_det_ke}
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\end{figure}
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\begin{figure}[htbp]
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\centering
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\includegraphics[width=0.7\textwidth]{figs/ke_pdg_det1UpStr}
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\includegraphics[width=0.7\textwidth]{figs/ke_pdg_det2UpStr}
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\caption{Kinetic energy and type of particles hitting STM detectors 1 (top),
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and 2 (bottom).}
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\label{fig:stm_det_ptype}
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\end{figure}
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\subsection{STM detector hit rate estimation}
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\label{sub:stm_detector_hit_rate_estimation}
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The average number of hits on a STM detector per POT is:
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\begin{equation}
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\frac{888 + 888}{2 \times 8 \times 10^{11}} = 8.7 \times 10^{-9}.
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\end{equation}
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There are 3.1 POTs per proton bunch, so the number of hits per bunch is:
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\begin{equation}
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8.7 \times 10^{-9} \times 3.1 \times 10^7 = 0.27
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\end{equation}
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The instantaneous hit rate, assuming an interval of \SI{1695}{\ns} between
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bunches, is:
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\begin{equation}
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\frac{0.27}{1695\times 10^{-9}} = \SI{159e3}{\Hz}
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\end{equation}
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\appendix
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\section{How to run the simulation and analyze data}
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\label{sec:how_to_run_the_simulation_and_analyze_data}
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\section{Muonic X-rays in Geant4}
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\label{sec:muonic_x_rays_in_geant4}
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The muonic energy levels and transition probabilities were calculated using
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a simple model described by Mukhopadhyay~\cite{Mukhopadhyay.1977}.
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\begin{itemize}
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\item Energies of K-shell electrons were precisely corrected based on
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that of hydrogen atom, taking finite size of the nucleus into account
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% \lstinputlisting[
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% language=c++, firstline=64, lastline=93,firstnumber=64,
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% breaklines=true, breakatwhitespace=true,
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% frame=single]{listings/G4EmCaptureCascade.cc}
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\begin{mdframed}
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\inputminted[
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breaklines=true,
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stepnumber=5,
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linenos=true,
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firstline=64,
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% fontsize=\footnotesize,
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lastline=93]{c++}{listings/G4EmCaptureCascade.cc}
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\end{mdframed}
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\item Energies of
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\end{itemize}
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\bibliographystyle{h-physrev}
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\bibliography{stm_study}
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\end{document}
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