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thesis/chapters/chap4_alcap_phys.tex
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@@ -410,10 +410,10 @@ data. There are two reasons for that:
\end{enumerate}
The first study was done by Morigana and Fry~\cite{MorinagaFry.1953} where
24,000 muon tracks were stopped in their nuclear emulsion which contains silver,
bromine, and other light elements, mainly nitrogen, carbon, hydrogen and
bromine AgBr, and other light elements, mainly nitrogen, carbon, hydrogen and
oxygen. The authors identified a capture on a light element as it would leave
a recoil
track of the nucleus. They found that for silver bromide AgBr, $(2.2 \pm
track of the nucleus. They found that for silver bromide, $(2.2 \pm
0.2)\%$ of the captures produced protons and $(0.5 \pm 0.1)\%$ produced alphas.
For light elements, the emission rate for proton and alpha are respectively
$(9.5 \pm 1.1)\%$ and $(3.4 \pm 0.7)\%$. Subsequently, Kotelchuk and
@@ -423,9 +423,13 @@ statistics and in fair agreement with Morigana and Fry
\begin{figure}[htb]
\centering
\includegraphics[width=0.65\textwidth]{figs/kotelchuk_proton_spectrum}
\caption{Early proton spectrum after muon capture in silver bromide AgBr
recorded using nuclear emulsion. Image is taken from
Ref.~\cite{KotelchuckTyler.1968}}
\caption{Proton spectrum after muon capture in silver bromide AgBr in
early experiments recorded using nuclear emulsion. The closed circles
are data points from Morigana and Fry~\cite{MorinagaFry.1953}, the
histogram is measurement result of Kotelchuk and
Tyler~\cite{KotelchuckTyler.1968}. Reprinted figure from
reference~\cite{KotelchuckTyler.1968}. Copyright 1968 by the American
Physical Society.}
\label{fig:kotelchuk_proton_spectrum}
\end{figure}
@@ -475,16 +479,18 @@ might be at work in this mass range.
target (closed circle) in the energy range above 40 MeV and an exponential
fit. The open squares are silicon data from Budyashov et
al.~\cite{BudyashovZinov.etal.1971}, the open triangles are magnesium data
from Balandin et al.~\cite{BalandinGrebenyuk.etal.1978}.}
from Balandin et al.~\cite{BalandinGrebenyuk.etal.1978}. Reprinted
figure from reference~\cite{KraneSharma.etal.1979}. Copyright 1979 by
the American Physical Society.}
\label{fig:krane_proton_spec}
\end{figure}
The aforementioned difficulties in charged particle measurements could be
solved using an active target, just like nuclear emulsion. Sobottka and
Wills~\cite{SobottkaWills.1968} took this approach when using a Si(Li) detector
to stop muons. They obtained a spectrum of charged particles up to 26
\si{\MeV}~in \cref{fig:sobottka_spec}. The peak below 1.4
\si{\MeV}~is due to the recoiling $^{27}$Al. The higher energy events
to stop muons. They obtained a spectrum of charged particles up to \SI{26}{\MeV}
in \cref{fig:sobottka_spec}. The peak below \SI{1.4}{\MeV}
is due to the recoiling $^{27}$Al. The higher energy events
including protons, deuterons and alphas constitute $(15\pm 2)\%$ of capture
events, which is consistent with a rate of $(12.9\pm1.4)\%$ from gelatine
observed by Morigana and Fry. This part has an exponential
@@ -507,7 +513,8 @@ silicon, and $(17\pm4)\%$ in copper.
\centering
\includegraphics[width=0.75\textwidth]{figs/sobottka_spec}
\caption{Charged particle spectrum from muon capture in a silicon detector,
image taken from Sobottka and Wills~\cite{SobottkaWills.1968}.}
measured by Sobottka and Wills~\cite{SobottkaWills.1968}. The plot is
reproduced from the original figure in reference~\cite{SobottkaWills.1968}.}
\label{fig:sobottka_spec}
\end{figure}
@@ -544,7 +551,7 @@ against the Coulomb barrier for the outgoing protons are given in
%and \cref{fig:wyttenbach_rate_23p}.
The classical Coulomb barrier $V$ they used are given by:
\begin{equation}
V = \frac{zZe^2}{r_0A^{\frac{1}{3}} + \rho},
V = \frac{zZe^2}{r_0A^{\frac{1}{3}} + \rho}\,,
\label{eqn:classical_coulomb_barrier}
\end{equation}
where $z$ and $Z$ are the charges of the outgoing particle and of the residual
@@ -552,11 +559,15 @@ nucleus respectively, $e^2 = 1.44 \si{\MeV}\cdot\textrm{fm}$, $r_0 = 1.35
\textrm{ fm}$, and $\rho = 0 \textrm{ fm}$ for protons were taken.
\begin{figure}[htb]
\centering
\includegraphics[width=0.48\textwidth]{figs/wyttenbach_rate_1p}
\includegraphics[width=0.505\textwidth]{figs/wyttenbach_rate_23p}
\caption{Activation results from Wyttenbach et
al.~\cite{WyttenbachBaertschi.etal.1978} for the $(\mu^-,\nu p)$,
$(\mu^-,\nu pn)$, $(\mu^-,\nu p2n)$ and $(\mu^-,\nu p3n)$ reactions.}
\includegraphics[width=0.48\textwidth]{figs/wyttenbach_rate_1p}
\includegraphics[width=0.505\textwidth]{figs/wyttenbach_rate_23p}
\caption{Activation results from Wyttenbach and
colleagues~\cite{WyttenbachBaertschi.etal.1978} for the $(\mu^-,\nu p)$,
$(\mu^-,\nu pn)$, $(\mu^-,\nu p2n)$ and $(\mu^-,\nu p3n)$ reactions. The
cross section of each individual channels decreases exponentially as the
Coulomb barrier for proton emission increases.
Reprinted figure from reference~\cite{WyttenbachBaertschi.etal.1978} with
permission from Elsevier.}
\label{fig:wyttenbach_rate_1p}
\end{figure}
%\begin{figure}[htb]
@@ -568,10 +579,10 @@ nucleus respectively, $e^2 = 1.44 \si{\MeV}\cdot\textrm{fm}$, $r_0 = 1.35
%\label{fig:wyttenbach_rate_23p}
%\end{figure}
Wyttenbach et al.\ saw that the cross section of each reaction decreases
Wyttenbach and colleagues saw that the cross section of each reaction decreases
exponentially with increasing Coulomb barrier. The decay constant for all
$(\mu^-,\nu pxn)$ is about 1.5 per \si{\MeV}~of Coulomb barrier. They
also commented a ratio for different de-excitation channels:
also observed a ratio for different de-excitation channels:
\begin{equation}
(\mu^-,\nu p):(\mu^-,\nu pn):(\mu^-,\nu p2n):(\mu^-,\nu p3n) = 1:6:4:4,
\label{eqn:wyttenbach_ratio}
@@ -581,7 +592,7 @@ the results from Vil'gel'mova et al.~\cite{VilgelmovaEvseev.etal.1971} as being
too high, but Measday~\cite{Measday.2001} noted it it is not
necessarily true since there has been suggestion from other experiments that
$(\mu^-, \nu p)$ reactions might become more important for light nuclei.
Measday also commented that the ratio~\eqref{eqn:wyttenbach_ratio} holds over
Measday noted that the ratio~\eqref{eqn:wyttenbach_ratio} holds over
a broad range of mass, but below $A=40$ the $(\mu^-,\nu p)$ reaction can vary
significantly from nucleus to nucleus.
% subsection experimental_status (end)
@@ -598,24 +609,25 @@ $\rho(p) \sim A/(B^2 + p^2)^2$; (II) Fermi gas at zero temperature; and (III)
Fermi gas at a finite temperature ($kT = 9$ \si{\MeV}).
A very good agreement with the experimental result for the alpha emission was
obtained with distribution (III), both in the absolute percentage and the energy
distribution (curve (III) in the left hand side of
\cref{fig:ishii_cal_result}). However, the calculated emission of protons
at the same temperature falls short by about 10
times compares to the data. The author also found that the distribution
(I) is unlikely to be suitable for proton emission, and using that distribution
for alpha emission resulted in a rate 15 times larger than observed.
obtained with distribution (III).
%, both in the absolute percentage and the energy
%distribution (curve (III) in the left hand side of
%\cref{fig:ishii_cal_result}).
However, the calculated emission rate of protons at the same temperature was 10
times smaller the experimental results from Morigana and Fry. The author
found the distribution (I) is unlikely to be suitable for proton emission,
and using that distribution
for alpha emission resulted in a rate 15 times larger than the observed rate.
\begin{figure}[htb]
\centering
\includegraphics[width=.49\textwidth]{figs/ishii_cal_alpha}
%\hspace{10mm}
\includegraphics[width=.49\textwidth]{figs/ishii_cal_proton}
\caption{Alpha spectrum (left) and proton spectrum (right) from Ishii's
calculation~\cite{Ishii.1959} in comparison with experimental data from
Morigana and Fry. Image is taken from Ishii's paper.}
\label{fig:ishii_cal_result}
\end{figure}
%\begin{figure}[htb]
%\centering
%\includegraphics[width=.49\textwidth]{figs/ishii_cal_alpha}
%\includegraphics[width=.49\textwidth]{figs/ishii_cal_proton}
%\caption{Alpha spectrum (left) and proton spectrum (right) from Ishii's
%calculation~\cite{Ishii.1959} in comparison with experimental data from
%Morigana and Fry. Image is taken from Ishii's paper.}
%\label{fig:ishii_cal_result}
%\end{figure}
Singer~\cite{Singer.1974} noted that by assuming a reduced effective mass for
the nucleon, the average excitation energy increases, but the proton
emission rate is not significantly improved and still could not explain the
@@ -650,7 +662,9 @@ spectrum and experimental data is shown in
\caption{Proton energy spectrum from muon capture in AgBr, the data in
histogram is from Morigana and Fry, calculation by Lifshitz and
Singer~\cite{LifshitzSinger.1978} showed contributions from the
pre-equilibrium emission and the equilibrium emission.}
pre-equilibrium emission and the equilibrium emission. Reprinted figure
from reference~\cite{LifshitzSinger.1978}. Copyright 1978 by the American
Physical Society.}
\label{fig:lifshitzsinger_cal_proton}
\end{figure}
@@ -689,20 +703,20 @@ al.~\cite{VilgelmovaEvseev.etal.1971} observed.
$^{31}_{15}$P & 6.7 & {(6.3)} & 35 & {$> 61$}&(91) \\
$^{39}_{19}$K & 19 & 32 \pm 6 & 67 & {} \\
$^{41}_{19}$K & 5.1 & {(4.7)} & 30 & {$> 28$} &(70)\\
%$^{51 }_{23}$V &3.7 &2.9 \pm 0.4 &25 &{$>20 \pm 1.8$}& (32)\\
%$^{55 }_{25}$Mn &2.4 &2.8 \pm 0.4 &16 &{$>26 \pm 2.5$}& (35)\\
%$^{59 }_{27}$Co &3.3 &1.9 \pm 0.2 &21 &{$>37 \pm 3.4$}& (50)\\
%$^{60 }_{28}$Ni &8.9 &21.4 \pm 2.3 &49 &40 \pm 5&\\
%$^{63 }_{29}$Cu &4.0 &2.9 \pm 0.6 &25 &{$>17 \pm 3 $}& (36)\\
%$^{65 }_{29}$Cu &1.2 &{(2.3)} &11 &{$>35 \pm 4.5$}& (36)\\
%$^{75 }_{33}$As &1.5 &1.4 \pm 0.2 &14 &{$>14 \pm 1.3$}& (19)\\
%$^{79 }_{35}$Br &2.7 &{} &22 & &\\
%$^{107}_{47}$Ag &2.3 &{} &18 & &\\
%$^{115}_{49}$In &0.63 &{(0.77)} &7.2 &{$>11 \pm 1$} &(12)\\
%$^{133}_{55}$Cs &0.75 &0.48 \pm 0.07 &8.7 &{$>4.9 \pm 0.5$} &(6.7)\\
%$^{165}_{67}$Ho &0.26 &0.30 \pm 0.04 &4.1 &{$>3.4 \pm 0.3$} &(4.6)\\
%$^{181}_{73}$Ta &0.15 &0.26 \pm 0.04 &2.8 &{$>0.7 \pm 0.1$} &(3.0)\\
%$^{208}_{82}$Pb &0.14 &0.13 \pm 0.02 &1.1 &{$>3.0 \pm 0.8$} &(4.1)\\
$^{51 }_{23}$V &3.7 &2.9 \pm 0.4 &25 &{$>20 \pm 1.8$}& (32)\\
$^{55 }_{25}$Mn &2.4 &2.8 \pm 0.4 &16 &{$>26 \pm 2.5$}& (35)\\
$^{59 }_{27}$Co &3.3 &1.9 \pm 0.2 &21 &{$>37 \pm 3.4$}& (50)\\
$^{60 }_{28}$Ni &8.9 &21.4 \pm 2.3 &49 &40 \pm 5&\\
$^{63 }_{29}$Cu &4.0 &2.9 \pm 0.6 &25 &{$>17 \pm 3 $}& (36)\\
$^{65 }_{29}$Cu &1.2 &{(2.3)} &11 &{$>35 \pm 4.5$}& (36)\\
$^{75 }_{33}$As &1.5 &1.4 \pm 0.2 &14 &{$>14 \pm 1.3$}& (19)\\
$^{79 }_{35}$Br &2.7 &{} &22 & &\\
$^{107}_{47}$Ag &2.3 &{} &18 & &\\
$^{115}_{49}$In &0.63 &{(0.77)} &7.2 &{$>11 \pm 1$} &(12)\\
$^{133}_{55}$Cs &0.75 &0.48 \pm 0.07 &8.7 &{$>4.9 \pm 0.5$} &(6.7)\\
$^{165}_{67}$Ho &0.26 &0.30 \pm 0.04 &4.1 &{$>3.4 \pm 0.3$} &(4.6)\\
$^{181}_{73}$Ta &0.15 &0.26 \pm 0.04 &2.8 &{$>0.7 \pm 0.1$} &(3.0)\\
$^{208}_{82}$Pb &0.14 &0.13 \pm 0.02 &1.1 &{$>3.0 \pm 0.8$} &(4.1)\\
\bottomrule
\end{tabular}
\end{center}
@@ -710,11 +724,11 @@ al.~\cite{VilgelmovaEvseev.etal.1971} observed.
reaction $^A_Z X (\mu,\nu p) ^{A-1}_{Z-2}Y$ and for inclusive proton
emission compiled by Measday~\cite{Measday.2001}. The calculated values
are from Lifshitz and Singer. The experimental data are mostly from
Wyttenbach et al.~\cite{WyttenbachBaertschi.etal.1978}. For inclusive emission
the experimental figures are lower limits, determined from the
actually measured channels. The figures in crescent parentheses are
estimates for the total inclusive rate derived from the measured exclusive
channels by the use of ratio in \eqref{eqn:wyttenbach_ratio}.}
Wyttenbach and colleagues~\cite{WyttenbachBaertschi.etal.1978}. The
inclusive emission the experimental figures are lower limits because only
a few decay channels could be studied. The figures in crescent parentheses
are estimates for the total inclusive rate derived from the measured
exclusive channels by the use of ratio in \eqref{eqn:wyttenbach_ratio}.}
\label{tab:lifshitzsinger_cal_proton_rate}
\end{table}
@@ -898,50 +912,63 @@ detectors will be assessed by detailed Monte Carlo study using Geant4.
\subsection{Goals and plan of the experiment}
\label{sub:goals_of_the_experiment}
Our experimental program is organised in three distinct work packages (WP),
The goal of the experiment is measure protons following nuclear muon capture
on aluminium:
\begin{enumerate}
\item emission rate,
\item and spectrum shape in the lower energy region down to \SI{2.5}{\MeV},
\item with a precision of about 5\%.
\end{enumerate}
The measured proton spectrum and rate will be used to assess the hit rate on
the tracking drift chamber of the COMET Phase-I.
The measurement of protons itself is part of the AlCap, where
experimental program is organised in three distinct work packages (WP),
directed by different team leaders, given in parentheses.
\begin{itemize}
\item[WP1:] (Kammel (Seattle), Kuno(Osaka)) \textbf{Charged
Particle Emission after Muon Capture.}\\ Protons emitted after nuclear muon
capture in the stopping target dominate the single-hit rates in the tracking
chambers for both the Mu2e and COMET Phase-I experiments. We plan to measure
both the total rate and the energy spectrum to a precision of 5\% down to
proton energies of \SI{2.5}{\MeV}.
\item[WP2:] (Lynn(PNNL), Miller(BU))
\textbf{Gamma and X-ray Emission after Muon Capture.}\\ A Ge detector will
be used to measure X-rays from the muonic atomic cascade, in order to provide
the muon-capture normalization for WP1, and is essential for very thin
stopping targets. It is also the primary method proposed for calibrating the
number of muon stops in the Mu2e and COMET experiments. Two additional
calibration techniques will also be explored; (1) detection of delayed gamma
rays from nuclei activated during nuclear muon capture, and (2) measurement
of the rate of photons produced in radiative muon decay. The first of these
would use a Ge detector and the second a NaI detector. The NaI
calorimeter will measure the rate of high energy photons from radiative muon
capture (RMC), electrons from muon decays in orbit (DIO), and photons from
radiative muon decay (RMD), as potential background sources for the
conversion measurement. As these rates are expected to be extremely low near
the conversion electron energy, only data at energies well below 100 MeV will
be obtained.
\item[WP3:] (Hungerford(UH), Winter(ANL)) \textbf{Neutron
Emission after Muon Capture.}\\ Neutron rates and spectra after capture in
Al and Ti are not well known. In particular, the low energy region below 10
MeV is important for determining backgrounds in the Mu2e/COMET detectors and
veto counters as well as evaluating the radiation damage to electronic
components. Carefully calibrated liquid scintillation detectors, employing
neutron-gamma discrimination and spectrum unfolding techniques, will measure
these spectra. The measurement will attempt to obtain spectra as low or lower
than 1 MeV up to 10 MeV. \\
\item[WP1:] (P. Kammel (University of Washington), Y. Kuno(Osaka University))
\textbf{Charged Particle Emission after Muon Capture.}\\ Protons emitted
after nuclear muon
capture in the stopping target dominate the single-hit rates in the tracking
chambers for both the Mu2e and COMET Phase-I experiments. We plan to measure
both the total rate and the energy spectrum to a precision of 5\% down to
proton energies of \SI{2.5}{\MeV}.
\item[WP2:] (J. Miller(Boston University))
\textbf{Gamma and X-ray Emission after Muon Capture.}\\ A germanium detector
will be used to measure X-rays from the muonic atomic cascade, in order to
provide
the muon-capture normalisation for WP1, and is essential for very thin
stopping targets. It is also the primary method proposed for calibrating the
number of muon stops in the Mu2e and COMET experiments. Two additional
calibration techniques will also be explored; (1) detection of delayed gamma
rays from nuclei activated during nuclear muon capture, and (2) measurement
of the rate of photons produced in radiative muon decay. The first of these
would use a germanium detector and the second a sodium iodine detector.
The sodium iodine
calorimeter will measure the rate of high energy photons from radiative muon
capture (RMC), electrons from muon decays in orbit (DIO), and photons from
radiative muon decay (RMD), as potential background sources for the
conversion measurement. As these rates are expected to be extremely low near
the conversion electron energy, only data at energies well below 100 MeV will
be obtained.
\item[WP3:] (E. Hungerford (University of Houston), P. Winter(Argonne
National Laboratory)) \textbf{Neutron
Emission after Muon Capture.}\\ Neutron rates and spectra after capture in
Al and Ti are not well known. In particular, the low energy region below 10
MeV is important for determining backgrounds in the Mu2e/COMET detectors and
veto counters as well as evaluating the radiation damage to electronic
components. Carefully calibrated liquid scintillation detectors, employing
neutron-gamma discrimination and spectrum unfolding techniques, will measure
these spectra. The measurement will attempt to obtain spectra as low or lower
than 1 MeV up to 10 MeV. \\
\end{itemize}
WP1 is the most developed
project in this program with most of the associated apparatus has been built and
optimized. We are ready to start this experiment in 2013, while preparing and
completing test measurements and simulations to undertake WP2 and WP3.
WP1 was the most developed project in this program with most of the associated
apparatus had been built and optimised. Therefore the measurement of proton has
been carried out in November and December 2013, while preparing and completing
test measurements and simulations to undertake WP2 and WP3.
The measurement of proton has been carried out in November and December 2013,
the details are described in following chapters.
% subsection goals_of_the_experiment (end)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% section the_alcap_experiment (end)