diff --git a/thesis/chapters/chap4_alcap_phys.tex b/thesis/chapters/chap4_alcap_phys.tex index cb4a9c3..0a33eb7 100644 --- a/thesis/chapters/chap4_alcap_phys.tex +++ b/thesis/chapters/chap4_alcap_phys.tex @@ -736,7 +736,7 @@ smaller in cases of Al and Cu, and about 10 times higher in case of AgBr \begin{center} \begin{tabular}{l l c} \toprule - \textbf{Nucleus} & \textbf{Exp.$\times 10^3$} & \textbf{MEC cal.$\times + \textbf{Nucleus} & \textbf{Experiment$\times 10^3$} & \textbf{Calculation$\times 10^3$}\\ \midrule Al & $1.38 \pm 0.09$ & 0.3\\ @@ -748,9 +748,10 @@ smaller in cases of Al and Cu, and about 10 times higher in case of AgBr \bottomrule \end{tabular} \end{center} - \caption{Probability of proton emission with $E_p \ge 40$ - \si{\MeV}~as calculated by Lifshitz and - Singer~\cite{LifshitzSinger.1988} in comparison with available data.} + \caption{Probability of proton emission with $E_p \ge \SI{40}{\MeV}$ + calculated by Lifshitz and + Singer~\cite{LifshitzSinger.1988} with the two-nucleon capture hypothesis + in comparison with available data.} \label{tab:lifshitzsinger_cal_proton_rate_1988} \end{table} % subsection theoretical_models (end) @@ -825,7 +826,7 @@ protons should be affordable. The proton absorber solves the problem of hit rate, but it degrades the reconstructed momentum resolution. Therefore its thickness and geometry should be carefully optimised. The limited information available makes it difficult to -arrive at a conclusive detector design. The proton emission rate could be 0.97\% +arrive at a conclusive detector design. The proton emission rate could be 4\% as calculated by Lifshitz and Singer~\cite{LifshitzSinger.1980}; or 7\% as estimated from the $(\mu^-,\nu pn)$ activation data and the ratio in \eqref{eqn:wyttenbach_ratio}; or as high as 15-20\% from silicon and neon. @@ -836,7 +837,8 @@ are adopted follow the silicon data from Sobottka and Will ~\cite{SobottkaWills.1968}. The spectrum shape is fitted with an empirical function given by: \begin{equation} - p(T) = A\left(1-\frac{T_{th}}{T}\right)^\alpha \exp{-\frac{T}{T_0})}, + p(T) = A\left(1-\frac{T_{th}}{T}\right)^\alpha + \exp{\left(-\frac{T}{T_0}\right)}, \label{eqn:EH_pdf} \end{equation} where $T$ is the kinetic energy of the proton in \si{\MeV}, and the fitted diff --git a/thesis/chapters/chap6_analysis.tex b/thesis/chapters/chap6_analysis.tex index fc18da0..b84f3eb 100644 --- a/thesis/chapters/chap6_analysis.tex +++ b/thesis/chapters/chap6_analysis.tex @@ -475,21 +475,22 @@ The yields of protons from \SIrange{4}{8}{\MeV} are: \end{align} The number of emitted protons is taken as average of the two yields: \begin{equation} - N_{\textrm{p unfold}} = (169.3 \pm 2.9) \times 10^3 + N_{\textrm{p unfold}} = (169.3 \pm 1.9) \times 10^3 \end{equation} \subsection{Number of nuclear captures} \label{sub:number_of_nuclear_captures} -\begin{figure}[htb] - \centering - \includegraphics[width=0.85\textwidth]{figs/al100_ge_spec} - \caption{X-ray spectrum from the aluminium target, the characteristic - $(2p-1s)$ line shows up at 346.67~keV} -\label{fig:al100_ge_spec} -\end{figure} +%\begin{figure}[!htb] + %\centering + %\includegraphics[width=0.85\textwidth]{figs/al100_ge_spec} + %\caption{X-ray spectrum from the aluminium target, the characteristic + %$(2p-1s)$ line shows up at 346.67~keV} +%\label{fig:al100_ge_spec} +%\end{figure} -The X-ray spectrum on the germanium detector is shown on -\cref{fig:al100_ge_spec}. Fitting the double peaks on top of a first-order +%The X-ray spectrum on the germanium detector is shown on +%\cref{fig:al100_ge_spec}. +Fitting the double peaks on top of a first-order polynomial gives the X-ray peak area of $5903.5 \pm 109.2$. With the same procedure as in the case of the active target, the number stopped muons and the number of nuclear captures are: @@ -508,7 +509,15 @@ The proton emission rate in the range from \SIrange{4}{8}{\MeV} is therefore: \end{equation} The total proton emission rate can be estimated by assuming a spectrum shape -with the same parameterisation as in \eqref{eqn:EH_pdf}. The fit parameters +with the same parameterisation as in \eqref{eqn:EH_pdf}. The +\eqref{eqn:EH_pdf} function has a power rising edge, and a exponential decay +falling edge. The falling edge has only one decay component and is suitable to +describe the proton spectrum with the equilibrium emission only assumption. +The pre-equilibrium emission contribution should be small for low-$Z$ material, +for aluminium the contribution of this component is 2.2\% according to +Lifshitz and Singer~\cite{LifshitzSinger.1980}. + +The fitted results are shown in \cref{fig:al100_parameterisation} and \cref{tab:al100_fit_pars}. The average spectrum is obtained by taking the average of the two unfolded spectra from the left and right arms. The fitted parameters are compatible @@ -534,7 +543,7 @@ protons. The total proton emission rate is therefore estimated to be $3.5\times $A \times 10^{-5}$ & 2.0 \pm 0.7 & 1.3 \pm 0.1 & 1.5 \pm 0.3\\ $T_{th}$ (\si{\keV}) & 1301 \pm 490 & 1966 \pm 68 & 1573 \pm 132\\ $\alpha$ & 3.2 \pm 0.7 & 1.2 \pm 0.1 & 2.0 \pm 1.2\\ - $T_{th}$ (\si{\keV}) & 2469 \pm 203 & 2641 \pm 106 & 2601 \pm 186\\ + $T_{0}$ (\si{\keV}) & 2469 \pm 203 & 2641 \pm 106 & 2601 \pm 186\\ \bottomrule \end{tabular} \end{center} @@ -597,7 +606,7 @@ presented in \cref{tab:al100_uncertainties_all}. \textbf{Item}& \textbf{Value} \\ \midrule Number of muons & 3.2\% \\ - Statistical from measured spectra & 1.6\% \\ + Statistical from measured spectra & 1.1\% \\ Systematic from unfolding & 5.0\% \\ Systematic from PID & \textless0.5\% \\ \midrule @@ -638,7 +647,7 @@ validated: \subsection{Proton emission rates and spectrum} \label{sub:proton_emission_rates_and_spectrum} The proton emission spectrum in \cref{sub:proton_emission_rate} peaks around -\SI{4}{\MeV} which is comparable to the Coulomb barrier for proton of +\SI{3.7}{\MeV} which is a little below the Coulomb barrier for proton of \SI{3.9}{\MeV} calculated using \eqref{eqn:classical_coulomb_barrier}. The spectrum has a decay constant of \SI{2.6}{\MeV} in higher energy region, makes the emission probability drop more quickly than silicon charged @@ -661,29 +670,48 @@ all energy is: R_{p \textrm{ total}} = (3.5 \pm 0.2)\%. \label{eqn:meas_total_rate} \end{equation} -No direct comparison of this result to existing experimental or -theoretical work is available. Indirectly, it is compatible with the figures -calculated by Lifshitz and + +\subsubsection{Comparison to theoretical and other experimental results} +\label{ssub:comparison_to_theoretical_and_other_experimental_results} +There is no existing experimental or theoretical work that could be directly +compared with the obtained proton emission rate. Indirectly, it is compatible +with the figures calculated by Lifshitz and Singer~\cite{LifshitzSinger.1978, LifshitzSinger.1980} listed in \cref{tab:lifshitzsinger_cal_proton_rate}. It is significantly larger than the rate of 0.97\% for the $(\mu,\nu p)$ channel, and does not exceed the inclusion rate for all channels $\Sigma(\mu,\nu p(xn))$ at 4\%, -leaving some room for other modes such as $(\mu,\nu d)$ or $(\mu,\nu p2n)$. -Certainly, if the rate of deuterons can be extracted then the combined -emission rate of protons and deuterons could be compared directly with the -inclusive rate. +leaving some room for other modes such as emission of deuterons or tritons. +Certainly, when the full analysis is available, deuterons and tritons emission +rates could be extracted and the combined emission rate could be compared +directly with the inclusive rate. The result \eqref{eqn:meas_total_rate} is greater than the probability of the reaction $(\mu,\nu pn)$ measured by Wyttenbach et al.~\cite{WyttenbachBaertschi.etal.1978} at 2.8\%. It is expectable because the contribution from the $(\mu,\nu d)$ channel should be small since it needs to form a deuteron from a proton and a neutron. + +The rate of 3.5\% was estimated with an assumption that all protons are +emitted in equilibrium. With the exponential constant of \SI{2.6}{\MeV}, the +proton yield in the range from \SIrange{40}{70}{\MeV} is negligibly small +($\sim\num{E-8}$). However, Krane and colleagues reported a significant yield +of 0.1\% in that region~\cite{KraneSharma.etal.1979}. The energetic proton +spectrum shape also has a different exponential constant of \SI{7.5}{\MeV}. One +explanation for these protons is that they are emitted by other mechanisms, +such as capture on two-nucleon cluster suggested by Singer~\cite{Singer.1961} +(see \cref{sub:theoretical_models} and +\cref{tab:lifshitzsinger_cal_proton_rate_1988}). Despite being sizeable, the +yield of high energy protons is still small (3\%) in compared with the result +in \eqref{eqn:meas_total_rate}. + %The $(\mu^-,\nu p):(\mu^-,\nu pn)$ ratio is then roughly 1:1, not 1:6 as in %\eqref{eqn:wyttenbach_ratio}. -Compared with emission rate from silicon, the result -\eqref{eqn:meas_total_rate} is indeed much smaller. It is even lower than -the rate of the no-neutron reaction $(\mu,\nu p)$. This can be explained as +\subsubsection{Comparison to the silicon result} +\label{ssub:comparison_to_the_silicon_result} +The probability of proton emission per nuclear capture of 3.5\% is indeed much +smaller than that of silicon. It is even lower than the rate of the no-neutron +reaction $(\mu,\nu p)$. This can be explained as the resulted nucleus from muon capture on silicon, $^{28}$Al, is an odd-odd nucleus and less stable than that from aluminium, $^{27}$Mg. The proton separation energy for $^{28}$Al is \SI{9.6}{\MeV}, which is significantly diff --git a/thesis/chapters/chap7_results.tex b/thesis/chapters/chap7_results.tex index 64da318..fd471d8 100644 --- a/thesis/chapters/chap7_results.tex +++ b/thesis/chapters/chap7_results.tex @@ -43,9 +43,11 @@ recorded (see \cref{fig:cdc_toy_mc_p_spec_500um}). \begin{figure}[!htb] \centering \includegraphics[width=0.75\textwidth]{figs/cdc_toy_mc_p_spec_500um} - \caption{Toy MC study of the CDC hit rate due to protons. The absorber - thickness was set at \SI{0.5}{\mm} in this plot.} - \label{fig:cdc_toy_mc_p_spec_500um} + \caption{Proton energy spectra at different stages from birth to the + sensitive volume of the CDC. The baseline design of \SI{0.5}{\mm} thick + absorber and \SI{0.5}{\mm} thick inner wall was used to produce this + plot.} + \label{fig:cdc_toy_mc_p_spec_500um} \end{figure} A muon stopping rate of \SI{1.3E9}{\Hz} is assumed as in the COMET Phase I's @@ -55,34 +57,44 @@ layer due to these protons with different absorber thickness are shown in \cref{tab:proton_cdc_hitrate}. \begin{table}[htb] \begin{center} - \begin{tabular}{S S S S} + \begin{tabular}{S S S S S} \toprule {\textbf{Absorber}} &{\textbf{Inner wall}} & {\textbf{Total CFRP}}& - {\textbf{Proton}}\\ + {\textbf{Proton}} & {\textbf{Momentum}}\\ {\textbf{thickness}} &{\textbf{thickness}} & {\textbf{thickness}}& - {\textbf{hit rate}}\\ - {(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})}\\ + {\textbf{hit rate}} &{\textbf{spread $\Delta p$}}\\ + {(\si{\mm})} & {(\si{\mm})} & {(\si{\mm})} & {(\si{\Hz})} + & {(\si{\keV\per\cc)}}\\ \midrule - 1 &0.5&1.5 & 2\\ - 0.5 &0.5&1.0 & 126\\ - 0 &0.5&0.5 & 1436\\ - 0 &0.3&0.3 & 8281\\ - 0 &0.1&0.1 & 15011\\ + 1 &0.5&1.5 & 2 & 195\\ + 0.5 &0.5&1.0 & 126 & 167\\ + 0 &0.5&0.5 & 1436 & 133\\ + 0 &0.3&0.3 & 8281 & {-}\\ + 0 &0.1&0.1 & 15011& {-}\\ \bottomrule \end{tabular} \end{center} - \caption{CDC proton hit rates} + \caption{CDC proton hit rates at different configuration of proton absorber + and inner wall. The momentum spreads for \SI{0.5}{\mm} thick inner wall are + taken from \cref{tab:comet_absorber_impact}.} \label{tab:proton_cdc_hitrate} \end{table} At the baseline design of \SI{0.5}{\mm}, the hit rate is only \SI{126}{\Hz}, much smaller than the current estimation at \SI{34}{\kHz}. Even without the -absorber, proton hit rate remains low at \SI{1.4}{\kHz}. Therefore a proton -absorber is not needed for the COMET Phase I's CDC. +absorber, proton hit rate remains low at \SI{1.4}{\kHz}. +%Therefore a proton +%absorber is not needed for the COMET Phase I's CDC. -Without the proton absorber, the momentum spread of the signal electron -reduces from \SI{167}{\keV} to \SI{131}{\keV}. If a lower momentum spread is -desired, it is possible to reduce the thickness of the inner wall. The last +If the proton absorber is not used, the momentum spread of the signal electron +reduces from \SI{167}{\keV} to \SI{131}{\keV}. In case a lower momentum spread +is desired, it is possible to reduce the thickness of the inner wall. The last two rows of \cref{tab:proton_cdc_hitrate} show that even with thinner walls at \SI{0.3}{\mm} and \SI{0.1}{\mm} the hit rate by protons are still at -manageable levels. +manageable levels. However, reducing the wall thickness would be governed by +other requirements such as mechanical structure and gas-tightness. + +In summary, the toy MC study with the preliminary proton rate and spectrum +shows that a proton absorber is not needed. It confirms the known fact that the +estimation used in COMET Phase-I is conservative, and provides a solid +prediction of the hit rate caused by protons. diff --git a/thesis/chapters/chap8_conclusions.tex b/thesis/chapters/chap8_conclusions.tex index ca92006..4c27f09 100644 --- a/thesis/chapters/chap8_conclusions.tex +++ b/thesis/chapters/chap8_conclusions.tex @@ -1,6 +1,6 @@ \chapter{Conclusions} \label{cha:conclusions} -AlCap is an experiment proposed at PSI to study charged particles, neutrons +The AlCap is an experiment proposed at PSI to study charged particles, neutrons and photons emitting after nuclear muon capture on aluminium. These measurements are important for backgrounds and hit rates estimation of the new generation of \mueconv experiments, COMET and Mu2e. In the first stage of the @@ -9,23 +9,33 @@ dominated by low energy protons following muon capture on an aluminium target, which has never been measured. The first run of the AlCap which aims for proton measurement has been carried -out in 2013. Data analysis is in progress. An initial analysis on partial data -was done with the main results are: +out in 2013. Data analysis is in progress. Before finishing the complete AlCap +analysis, an initial analysis on partial data +was made. The main results are: \begin{enumerate} - \item Demonstration of the analysis chain from raw waveforms to physics - events; - \item Validation of the experimental method including: number of nuclear + \item demonstration of the analysis chain from trigger-less waveforms to + correlated physics events; + \item validation of the experimental method including: number of nuclear capture muons normalisation by muonic X-ray measurement, charged particle identification by specific energy loss, and unfolding of the proton energy spectrum using the iterative Bayesian method; - \item Obtaining preliminary results on proton emission rate and spectrum: - the proton spectrum has a peak at \SI{4}{\MeV}, then reduces exponentially + \item obtaining preliminary results on proton emission rate and spectrum: + the proton spectrum has a peak at \SI{3.7}{\MeV}, then reduces exponentially with a decay constant of \SI{2.6}{\MeV}. The partial emission rate in the energy range from \SIrange{4}{8}{\MeV} is $(1.7 \pm 0.1)\%$, and the total emission rate assuming the shape holds for the whole spectrum is $(3.5\pm0.2)$. \end{enumerate} +The emission rate is consistent with the lower limit of 2.8\% set by +Wyttenbach et al.~\cite{WyttenbachBaertschi.etal.1978}. It is also compatible +with the theoretical calculation by Lifshitz and +Singer~\cite{LifshitzSinger.1980}. Compared with the emission rate from +silicon, our result is smaller. + The proton rate and spectrum have been used to optimise the planned proton absorber for the drift chamber of the COMET Phase-I. The resulted proton hit -rate with the baseline configuration is very small compared with the current -figure. It is safe to remove the proton absorber altogether. +rate with the baseline configuration is very small compared with the current +figure. It is safe to remove the proton absorber altogether. This would make +a strong impact to the drift chamber design. The AlCap experiment is going to +submit a beam time request for the 2015 run to collect more data and other +measurements for neutrons and gamma rays. diff --git a/thesis/chapters/frontmatter.tex b/thesis/chapters/frontmatter.tex index 1dabec7..f185e9a 100644 --- a/thesis/chapters/frontmatter.tex +++ b/thesis/chapters/frontmatter.tex @@ -32,7 +32,7 @@ aluminium have been carried out in the 2013 run. The second run to study neutrons and photons is planned in 2015. The preliminary results from the analysis of the 2013 run are presented in this -thesis. The measured proton spectrum peaks at \SI{4}{\MeV} and decays +thesis. The measured proton spectrum peaks at \SI{3.7}{\MeV} and decays exponentially with the decay constant of \SI{2.6}{\MeV}. The emission rate of protons in the energy range from \SIrange{4}{8}{\MeV} is $(1.7\pm0.1)\%$. The total proton emission rate is estimated to be diff --git a/thesis/mythesis.sty b/thesis/mythesis.sty index 9bdb285..47b7e24 100644 --- a/thesis/mythesis.sty +++ b/thesis/mythesis.sty @@ -12,7 +12,7 @@ inner=1.25in, outer=1in, twoside]{geometry} %$ Hyper-link .. \RequirePackage[% -colorlinks=true,% color links instead of using boxes +colorlinks=false,% color links instead of using boxes linkcolor=red,% color for internal (intra-document) links citecolor=green,% color for bibliographic links urlcolor=blue,% color for URL links