diff --git a/r15a_xray/figs/r15a_setup_photo.png b/r15a_xray/figs/r15a_setup_photo.png index 99bf206..b9ae5f4 100644 Binary files a/r15a_xray/figs/r15a_setup_photo.png and b/r15a_xray/figs/r15a_setup_photo.png differ diff --git a/r15a_xray/tex/analysis.tex b/r15a_xray/tex/analysis.tex index 322c190..31b817b 100644 --- a/r15a_xray/tex/analysis.tex +++ b/r15a_xray/tex/analysis.tex @@ -1,2 +1,146 @@ \section{Data analysis} +\subsection{Digital pulse processing} +\label{sub:digital_pulse_processing} +Since we recorded all detector outputs using digitizers, offline digital pulse +processing is needed to extract energy and timing information. Typical output +pulses from HPGe and \ce{LaBr3} detectors are shown in +\cref{fig:typical_pulses}. +\begin{center} + \begin{figure}[tbp] + \centering + \includegraphics[width=1.0\textwidth]{figs/typical_pulses} + \caption{Typical output pulses of HPGe and \ce{LaBr3} detectors: energy + output HPGe high gain (top left), energy output HPGe low gain (top + right), timing output HPGe (bottom left), and \ce{LaBr3} (bottom right). + Each clock tick corresponds to \SI{10}{\ns} and \SI{2}{\ns} for top and + bottom plots, respectively.} + \label{fig:typical_pulses} + \end{figure} +\end{center} + +The timing pulses from the HPGe detector were not used in this analysis because +they are too long and noisy (see bottom left \cref{fig:typical_pulses}). +Energy of the HPGe detector is taken as amplitude of spectroscopy amplifier +outputs, its timing is determined by the clock tick where the trace passes +\SI{30}{\percent} of the amplitude. The timing resolution is \SI{235}{\ns} +using this method. + +\subsection{Calibrations} +\label{sub:calibrations} +The HPGe detector energy scales and acceptance were calibrated +using \ce{^{152}Eu}, \ce{^{60}Co}, \ce{^{88}Y} sources placed at the target +position. There was a separate run for background radiation. + +Energy resolutions are better than \SI{3.2}{\keV} for all calibrated peaks. +\begin{center} + \begin{figure}[htbp] + \centering + \includegraphics[width=1.0\textwidth]{figs/hpge_ecal} + \caption{Energy calibration spectra for the HPGe detector.} + \label{fig:hpge_ecal} + \end{figure} +\end{center} + +The detector acceptance above \SI{200}{\kilo\eV} were fitted using an empirical +function: +\begin{equation} + A = c_1 \times E ^ {c_2}, +\end{equation} +where $c_1 = 0.1631$, $c_2 = -0.9257$, and $E$ is photon energy in \si{\keV}. +Interpolation gives detector acceptance at the peaks of interest as shown in +\cref{tab:hpge_acceptance}. + +\begin{center} + \begin{figure}[htbp] + \centering + \includegraphics[width=1.0\textwidth]{figs/hpge_higain_acceptance} + \caption{Acceptance of the HPGe as a function of photon energy.} + \label{fig:hpge_higain_acceptance} + \end{figure} +\end{center} + +\begin{table}[tbp] +\centering +\caption{HPGe acceptance for photons of interest} +\label{tab:hpge_acceptance} +\begin{tabular}{@{}cccc@{}} +\toprule +\multicolumn{2}{c}{\textbf{\begin{tabular}[c]{@{}c@{}}Photon energy\\ {[}keV{]}\end{tabular}}} & \textbf{Acceptance} & \textbf{Error} \\ +\midrule +$2p-1s$ & 346.8 & \num{8.75E-4} &\num{4.0e-5} \\ +\ce{^{27}Mg} & 843.7 & \num{3.40E-4} &\num{0.9e-5} \\ + % & 1014.4 & \num{2.69e-4} &\num{1.07e-5} \\ +\ce{^{nat}Ti} & 931.96 & \num{3.06E-4} &\num{0.8e-5} \\ +\ce{^{26}Mg}* & 1088.7 & \num{1.51e-4} &\num{0.7e-5} \\ +% 0 346.828 0.000875 0.000040 +% 1 399.268 0.000753 0.000030 +% 2 400.177 0.000751 0.000030 +% 3 476.800 0.000624 0.000022 +% 4 843.740 0.000340 0.000009 +% 5 930.000 0.000306 0.000008 +% 6 931.000 0.000306 0.000008 +% 7 932.000 0.000306 0.000008 +% 8 1014.420 0.000279 0.000008 +% 9 1808.660 0.000151 0.000007 +\bottomrule +\end{tabular} +\end{table} + +\subsection{Number of stopped muons} +% TODO: justification for taking just number from muon counter + +The number of stopped muons are taken as number of muons seen by the muon +counter, since we used thick targets the muon beam is believed to stop +completely at the middle of the targets. This assumption is verified for the +aluminum target where count from muon counter was consistent with number of +stopped muons calculated from number of $(2p-1s)$ X-rays. + +\subsection{Muonic X-ray spectra} +We use the HPGe spectra to look for characteristic muonic X-rays from elements +of interest. Energies of these muonic X-rays are listed +in~\cref{tab:hpge_acceptance}. + +\subsubsection{Titanium} +We are looking at X-rays from $(2p-1s)$ transitions in titanium. Natural +titanium has 5 stable isotopes: \ce{^{46}Ti}, \ce{^{47}Ti}, \ce{^{48}Ti}, +\ce{^{49}Ti}, and \ce{^{50}Ti}, with the \ce{^{48}Ti} being the +most abundant at 73.72\%. The fine splitting between muonic $2p_{3/2} +$ and $2p_{1/2}$ levels in these stable isotopes are about +\SI{2}{keV}~\cite{Wohlfahrt1981}, comparable to the resolution of our HPGe +detector. The $(2p-1s)$ X-rays therefore show up as a broad, asymmetric peak +with a longer tail on the low energy side. The peak is fitted as two +Gaussian peaks on top of a first-order polynomial. + +\subsection{Fraction of muon captured by a nucleus} +An atomic captured muon at the 1S state has only two choices, either to decay +in orbit or to be captured on the nucleus. The total disappearance rate for +negative muon, $\Lambda_{tot}$, is given by: +\begin{equation} + \Lambda_{tot} = \Lambda_{cap} + Q \Lambda_{free}, + \label{eq:mu_total_capture_rate} +\end{equation} +where $\Lambda_{cap}$ and $\Lambda_{free}$ are nuclear capture rate and free +decay rate, respectively, and $Q$ is the Huff factor, which is corrects for the +fact that muon decay rate in a bound state is reduced because of the binding +energy reduces the available energy. + +Using mean lifetime measured by Suzuki et.al.~\cite{SuzukiMeasday.etal.1987} +and fractions of muons captured by element of interest are calculated and +listed in~\cref{tab:capture_frac}. +\begin{table}[tbp] + \centering + \caption{Nuclear capture probability calculated from mean lifetimes taken + from measurements of Suzuki et.al.~\cite{SuzukiMeasday.etal.1987}} + \label{tab:capture_frac} + \begin{tabular}{cccc} + \toprule + Element & Mean lifetime & Huff factor & Nuclear capture\\ + & [\si{ns}] & & probability [\%]\\ + \midrule + \ce{^{nat}Al} & \num{864.0 \pm 1.0} & \num{0.993} &\num{60.95(5)} \\ + \ce{^{nat}Ti} & \num{329.3 \pm 1.3} & \num{0.981} &\num{85.29(6)} \\ + \ce{^{nat}W} & \num{78.4 \pm 1.5} & \num{0.860} &\num{96.93(6)} \\ + \bottomrule + \end{tabular} +\end{table} diff --git a/r15a_xray/tex/intro.tex b/r15a_xray/tex/intro.tex index c48012b..1a18f99 100644 --- a/r15a_xray/tex/intro.tex +++ b/r15a_xray/tex/intro.tex @@ -1,2 +1,11 @@ \section{Introduction} -Why are we even doing this measurement? Here is a very thorough study~\cite{Zinatulina2019} +Why are we even doing this measurement? +\begin{itemize} + \item targets for mu-e conversion experiments + \item why did we measure \ce{W}, \ce{H_2O}, \ldots: background for Xrays of + interest in Mu2e + \item existing data? focused on nuclear charge radii, did not report muonic + X-ray yields. This is true for \ce{^{nat}Ti}~\cite{Wohlfahrt1981} + +\end{itemize} + diff --git a/r15a_xray/tex/results.tex b/r15a_xray/tex/results.tex index c486525..40a8319 100644 --- a/r15a_xray/tex/results.tex +++ b/r15a_xray/tex/results.tex @@ -1,2 +1,28 @@ \section{Results and discussions} +\subsection{Titanium} +Number of stopped muons in the natural titanium target was: +\begin{equation} + N_{\mu} = (88296 \pm 9) \times 10^3 \,. + \label{eqn:Nmu_Ti_Tsc} +\end{equation} +Fitting the peak around \SI{931}{keV} in the photon spectrum gives the +center of gravity at \SI{931.6 \pm 0.7}{keV} (see~\cref{fig:ti_931keV_fit}), +consistent with previously reported value~\cite{Wohlfahrt1981}. +Number of $(2p-1s)$ X-rays in the \SI{931.6}{keV} peak is: +\begin{equation} + N_{931.6} = (20750 \pm 764) \,. +\end{equation} + +\begin{figure}[tbp] + \centering + \includegraphics[width=0.8\textwidth]{figs/ti_931keV_fit} + \caption{Fitting $(2p-1s)$ peaks} + \label{fig:ti_931keV_fit} +\end{figure} + +The emission rate of the $(2p-1s)$ muonic X-rays is calculated as: +\begin{equation} + R_{Ti} = \frac{N_{931.6}}{A_{931.6} \times N_{\mu} \times f_{capTi}} = 0.90 + \pm 0.04 \,. +\end{equation} diff --git a/r15a_xray/tex/setup.tex b/r15a_xray/tex/setup.tex index 3cf13a0..c474365 100644 --- a/r15a_xray/tex/setup.tex +++ b/r15a_xray/tex/setup.tex @@ -5,14 +5,14 @@ The 2015 summer run focused on the detection of neutral particles: low energy X-ray, gamma ray and neutron emission after the muon is captured by the nucleus. -The X-rays and gamma rays of interest are: -\begin{itemize} - \item muonic $2p-1s$ transition in aluminum: \SI{346.8}{\kilo\eV} - \item \SI{843.7}{\kilo\eV} gamma from the $\beta^-$ decay of \ce{^{27}Mg} - (half-life: \SI{9.46}{\min}) - \item \SI{1808.7}{\kilo\eV} gamma from the first excited state of - \ce{^{26}Mg} -\end{itemize} +% The X-rays and gamma rays of interest are: +% \begin{itemize} + % \item muonic $2p-1s$ transition in aluminum: \SI{346.8}{\kilo\eV} + % \item \SI{843.7}{\kilo\eV} gamma from the $\beta^-$ decay of \ce{^{27}Mg} + % (half-life: \SI{9.46}{\min}) + % \item \SI{1808.7}{\kilo\eV} gamma from the first excited state of + % \ce{^{26}Mg} +% \end{itemize} Low momentum muons (less than \SI[]{40}{\mega\eVperc}) were stopped in a target after passing a muon counter @@ -58,11 +58,16 @@ Experimental layout is shown in \cref{fig:R2015a_setup}. \begin{center} \begin{figure}[tbp] \centering - \includegraphics[width=0.70\textwidth]{figs/r15a_setup_photo} - \caption{Layout of the AlCap 2015 summer run. Muons entered from the top of - the image. The LYSO detector is not visible in this image, which is - located further out in the bottom of the image.} - \label{fig:R2015a_setup} + \begin{minipage}{0.45\textwidth} + \includegraphics[width=1.0\textwidth]{figs/r15a_setup_photo} + \end{minipage} + \begin{minipage}{0.45\textwidth} + \includegraphics[width=1.0\textwidth]{figs/alcap_r15a_setup} + \end{minipage} + \caption{Layout of the AlCap experiment in the summer 2015 run. Negative + muons entered from the top of the photo. The LYSO detector is not visible + in this image, which is located further out in the bottom of the image.} + \label{fig:r15a_setup} \end{figure} \end{center} @@ -70,4 +75,6 @@ There were several runs with different targets made of aluminum, titanium, lead, water. All targets were sufficiently thick to stop the muon beam with momenta up to \SI{40}{\mega\eVperc}. +TODO: a table of targets and details + diff --git a/r15a_xray/xray.bib b/r15a_xray/xray.bib index 39508cf..147b77d 100644 --- a/r15a_xray/xray.bib +++ b/r15a_xray/xray.bib @@ -30,6 +30,32 @@ url = {https://link.aps.org/doi/10.1103/PhysRevC.23.533}, } +@Article{SuzukiMeasday.etal.1987, + author = {Suzuki, T and Measday, David F and Roalsvig, JP}, + title = {Total nuclear capture rates for negative muons}, + journal = {Physical Review C}, + year = {1987}, + volume = {35}, + number = {6}, + pages = {2212}, + file = {Published version:SuzukiMeasday.etal.1987.pdf:PDF}, + owner = {NT}, + publisher = {APS}, + timestamp = {2014-07-13}, + url = {http://journals.aps.org/prc/abstract/10.1103/PhysRevC.35.2212}, +} + +@Article{refId0, + author = {{Zinatulina, Daniya} and {Brian\c{c}on, Chantal} and {Brudanin, Victor} and {Egorov, Viacheslav} and {Perevoshchikov, Lev} and {Shirchenko, Mark} and {Yutlandov, Igor} and {Petitjean, Claude}}, + title = {Electronic catalogue of muonic X-rays}, + journal = {EPJ Web Conf.}, + year = {2018}, + volume = {177}, + pages = {03006}, + doi = {10.1051/epjconf/201817703006}, + url = {https://doi.org/10.1051/epjconf/201817703006}, +} + @Comment{jabref-meta: databaseType:bibtex;} @Comment{jabref-meta: grouping: