nam/writeup
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

fix chap4

Browse Source
This commit is contained in:
nam
2014-10-11 14:31:27 +09:00
parent 27ab5737ff
commit 7eabb23a86
3 changed files with 65 additions and 63 deletions
Download Patch File Download Diff File Expand all files Collapse all files

121
thesis/chapters/chap4_alcap_phys.tex
View File

@@ -347,18 +347,18 @@ $n_{avg} = (0.3 \pm 0.02)A^{1/3}$~\cite{Singer.1974}.
The neutron emission can be explained by several mechanisms:
\begin{enumerate}
\item Direct emission follows reaction~\eqref{eq:mucap_proton}: these neutrons
have fairly high energy, from a few \si{\mega\electronvolt}~to as high as 40--50
\si{\mega\electronvolt}.
have fairly high energy, from a few \si{\si{\MeV}}~to as high as 40--50
\si{\si{\MeV}}.
\item Indirect emission through an intermediate compound nucleus: the energy
transferred to the neutron in the process~\eqref{eq:mucap_proton} is 5.2
\si{\mega\electronvolt} if the initial proton is at rest, in nuclear
\si{\si{\MeV}} if the initial proton is at rest, in nuclear
environment, protons have a finite momentum distribution, therefore the
mean excitation energy of the daughter nucleus is around 15 to 20
\si{\mega\electronvolt}~\cite{Mukhopadhyay.1977}. This is above the nucleon
\si{\si{\MeV}}~\cite{Mukhopadhyay.1977}. This is above the nucleon
emission threshold in all complex nuclei, thus the daughter nucleus can
de-excite by emitting one or more neutrons. In some actinide nuclei, that
excitation energy might trigger fission reactions. The energy of indirect
neutrons are mainly in the lower range $E_n \le 10$ \si{\mega\electronvolt}
neutrons are mainly in the lower range $E_n \le 10$ \si{\si{\MeV}}
with characteristically exponential shape of evaporation process. On top of
that are prominent lines might appear where giant resonances occur.
\end{enumerate}
@@ -382,7 +382,7 @@ data. There are two reasons for that:
neutron emission. The rate is about 15\% for light nuclei and
reduces to a few percent for medium and heavy nuclei.
\item The charged particles are short ranged: the emitted protons,
deuterons and alphas are typically low energy (2--20~\mega\electronvolt).
deuterons and alphas are typically low energy ( \SIrange{2}{20}{\MeV}).
But a relatively thick target is normally needed in order to achieve
a reasonable muon stopping rate and charged particle statistics. Therefore,
emulsion technique is particularly powerful.
@@ -411,9 +411,9 @@ statistics and in fair agreement with Morigana and Fry
Protons with higher energy are technically easier to measure, but because of
the much lower rate, they can only be studied at meson facilities. Krane and
colleagues~\cite{KraneSharma.etal.1979} measured proton emission from
aluminium, copper and lead in the energy range above 40 \mega\electronvolt~and
aluminium, copper and lead in the energy range above \SI{40}{\MeV} and
found a consistent exponential shape in all targets. The integrated yields
above 40 \mega\electronvolt~are in the \sn{}{-4}--\sn{}{-3} range (see
above \SI{40}{\MeV} are in the \sn{}{-4}--\sn{}{-3} range (see
Table~\ref{tab:krane_proton_rate}), a minor contribution to total proton
emission rate.
\begin{table}[htb]
@@ -462,16 +462,16 @@ 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
\mega\electronvolt~in Figure~\ref{fig:sobottka_spec}. The peak below 1.4
\mega\electronvolt~is due to the recoiling $^{27}$Al. The higher energy events
\si{\MeV}~in Figure~\ref{fig:sobottka_spec}. The peak below 1.4
\si{\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
decay shape with a decay constant of 4.6 \mega\electronvolt. Measday
decay shape with a decay constant of 4.6 \si{\MeV}. Measday
noted~\cite{Measday.2001} the fractions of events in
the 26--32 \mega\electronvolt~range being 0.3\%, and above 32
\mega\electronvolt~range being 0.15\%. This figure is in agreement with the
integrated yield above 40 \mega\electronvolt~from Krane et al.
the 26--32 \si{\MeV}~range being 0.3\%, and above 32
\si{\MeV}~range being 0.15\%. This figure is in agreement with the
integrated yield above 40 \si{\MeV}~from Krane et al.
In principle, the active target technique could be applied to other material
such as germanium, sodium iodine, caesium iodine, and other scintillation
@@ -480,7 +480,7 @@ identification like in nuclear emulsion, the best one can achieve after all
corrections is a sum of all charged particles. It should be noted here
deuterons can contribute significantly, Budyashov et
al.~\cite{BudyashovZinov.etal.1971} found deuteron components to be
$(34\pm2)\%$ of the charged particle yield above 18 \mega\electronvolt~in
$(34\pm2)\%$ of the charged particle yield above 18 \si{\MeV}~in
silicon, and $(17\pm4)\%$ in copper.
\begin{figure}[htb]
\centering
@@ -547,7 +547,7 @@ protons were taken.
Wyttenbach et al.\ 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 \mega\electronvolt~of Coulomb barrier. They
$(\mu^-,\nu pxn)$ is about 1.5 per \si{\MeV}~of Coulomb barrier. They
also commented 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,
@@ -572,7 +572,7 @@ nucleus is formed, and then it releases energy by statistical emission of
various particles. Three models for momentum distribution of protons in the
nucleus were used: (I) the Chew-Goldberger distribution
$\rho(p) \sim A/(B^2 + p^2)^2$; (II) Fermi gas at zero temperature; and (III)
Fermi gas at a finite temperature ($kT = 9$ \mega\electronvolt).
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
@@ -598,7 +598,7 @@ the nucleon, the average excitation energy will increase, but the proton
emission rate does not significantly improve and still could not explain the
large discrepancy. He concluded that the evaporation mechanism can account
for only a small fraction of emitted protons. Moreover, the high energy protons
of 25--50 \mega\electronvolt~cannot be explained by the evaporation mechanism.
of 25--50 \si{\MeV}~cannot be explained by the evaporation mechanism.
He and Lifshitz~\cite{LifshitzSinger.1978, LifshitzSinger.1980} proposed two
major corrections to Ishii's model:
\begin{enumerate}
@@ -611,14 +611,14 @@ major corrections to Ishii's model:
is possibility for particles to escape from the nucleus.
\end{enumerate}
With these improvements, the calculated proton spectrum agreed reasonably with
data from Morigana and Fry in the energy range $E_p \le 30$ \mega\electronvolt.
data from Morigana and Fry in the energy range $E_p \le 30$ \si{\MeV}.
Lifshitz and Singer noted the pre-equilibrium emission is more important for
heavy nuclei. Its contribution in light nuclei is about a few percent,
increasing to several tens of percent for $100<A<180$, then completely
dominating in very heavy nuclei. This trend is also seen in other nuclear
reactions at similar excitation energies. The pre-equilibrium emission also
dominates the higher-energy part, although it falls short at energies higher
than 30 \mega\electronvolt. The comparison between the calculated proton
than 30 \si{\MeV}. The comparison between the calculated proton
spectrum and experimental data is shown in
Fig.~\ref{fig:lifshitzsinger_cal_proton}.
\begin{figure}[htb]
@@ -670,7 +670,7 @@ higher than average, though not as high as Vil'gel'mora et
al.~\cite{VilgelmovaEvseev.etal.1971} observed.
For protons with higher energies in the range of
40--90 \mega\electronvolt~observed in the emulsion data as well as in later
40--90 \si{\MeV}~observed in the emulsion data as well as in later
experiments~\cite{BudyashovZinov.etal.1971,BalandinGrebenyuk.etal.1978,
KraneSharma.etal.1979}, Lifshitz and Singer~\cite{LifshitzSinger.1988}
suggested another contribution from capturing on correlated two-nucleon
@@ -700,7 +700,7 @@ smaller in cases of Al and Cu, and about 10 times higher in case of AgBr
\end{tabular}
\end{center}
\caption{Probability of proton emission with $E_p \ge 40$
\mega\electronvolt~as calculated by Lifshitz and
\si{\MeV}~as calculated by Lifshitz and
Singer~\cite{LifshitzSinger.1988} in comparison with available data.}
\label{tab:lifshitzsinger_cal_proton_rate_1988}
\end{table}
@@ -710,17 +710,17 @@ smaller in cases of Al and Cu, and about 10 times higher in case of AgBr
\label{sub:summary_on_proton_emission_from_aluminium}
There is no direct measurement of proton emission following
muon capture in the relevant energy for the COMET Phase-I of 2.5--10
\mega\electronvolt:
\si{\MeV}:
\begin{enumerate}
\item Spectrum wise, only one energy spectrum (Figure~\ref{fig:krane_proton_spec})
for energies above 40 \mega\electronvolt~is available from Krane et
for energies above 40 \si{\MeV}~is available from Krane et
al.~\cite{KraneSharma.etal.1979},
where an exponential decay shape with a decay constant of
$7.5 \pm 0.4$~\mega\electronvolt. At low energy range, the best one can get is
$7.5 \pm 0.4$~\si{\MeV}. At low energy range, the best one can get is
the charged particle spectrum, which includes protons, deuterons and alphas,
from the neighbouring element silicon (Figure~\ref{fig:sobottka_spec}).
This charged particle spectrum peaks around 2.5 \mega\electronvolt~and
reduces exponentially with a decay constant of 4.6 \mega\electronvolt.
This charged particle spectrum peaks around 2.5 \si{\MeV}~and
reduces exponentially with a decay constant of 4.6 \si{\MeV}.
\item The activation data from Wyttenbach et
al.~\cite{WyttenbachBaertschi.etal.1978} only gives rate of
$^{27}\textrm{Al}(\mu^-,\nu pn)^{25}\textrm{Na}$ reaction, and set a lower
@@ -748,9 +748,9 @@ A spectrum shape at this energy range is not available.
\label{sub:motivation_of_the_alcap_experiment}
As mentioned, protons from muon capture on aluminium might cause a very high
rate in the COMET Phase-I CDC. The detector is designed to accept particles
with momenta in the range of 75--120 \mega\electronvolt\per\cc.
with momenta in the range of 75--120 \si{\MeV\per\cc}.
Figure~\ref{fig:proton_impact_CDC} shows that protons with kinetic energies of
2.5--8 \mega\electronvolt~will hit the CDC. Such events are troublesome due to
2.5--8 \si{\MeV}~will hit the CDC. Such events are troublesome due to
their large energy deposition. Deuterons and alphas at that momentum range is
not of concern because they have lower kinetic energy and higher stopping
power, thus are harder to escape the muon stopping target.
@@ -758,9 +758,9 @@ power, thus are harder to escape the muon stopping target.
\centering
\includegraphics[width=0.85\textwidth]{figs/proton_impact_CDC}
\caption{Momentum-kinetic energy relation of protons, deuterons and alphas
below 10\mega\electronvolt. Shaded area is the acceptance of the COMET
below 10\si{\MeV}. Shaded area is the acceptance of the COMET
Phase-I's CDC. Protons with energies in the range of 2.5--8
\mega\electronvolt~are in the acceptance of the CDC. Deuterons and alphas at
\si{\MeV}~are in the acceptance of the CDC. Deuterons and alphas at
low energies should be stopped inside the muon stopping target.}
\label{fig:proton_impact_CDC}
\end{figure}
@@ -793,10 +793,10 @@ function given by:
where $T$ is the kinetic energy of the proton, and the fitted parameters are
$A=0.105\textrm{ MeV}^{-1}$, $T_{th} = 1.4\textrm{ MeV}$, $\alpha = 1.328$ and
$T_0 = 3.1\textrm{ MeV}$. The baseline
design of the absorber is 1.0 \milli\meter~thick
design of the absorber is 1.0 \si{\mm}~thick
carbon-fibre-reinforced-polymer (CFRP) which contributes
195~\kilo\electronvolt\per\cc~to the momentum resolution. The absorber also
down shifts the conversion peak by 0.7 \mega\electronvolt. This is an issue as
195~\si{\keV\per\cc}~to the momentum resolution. The absorber also
down shifts the conversion peak by 0.7 \si{\MeV}. This is an issue as
it pushes the signal closer to the DIO background region. For those reasons,
a measurement of the rate and spectrum of proton emission after muon capture is
required in order to optimise the CDC design.
@@ -804,41 +804,40 @@ required in order to optimise the CDC design.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Experimental method for proton measurement}
\label{sub:experimental_method}
We planned to use a low energy, narrow momentum spread available at PSI to
We planned to use a low-energy, narrow-momentum-spread available at PSI to
fight the aforementioned difficulties in measuring protons. The beam momentum
is tunable from 28 to 45~\mega\electronvolt\ so that targets at different
thickness from 25 to 100 \micro\meter\ can be studied. The $\pi$E1 beam line
could provide about \sn{}{3} muons\per\second\ at 1\% momentum spread, and
\sn{}{4} muons\per\second\ at 3\% momentum spread. With this tunable beam, the
stopping distribution of the muons is well-defined.
is tunable from \SIrange{28}{45}{\MeV} so that targets at different
thickness from \SIrange{25}{100}{\um} can be studied. The $\pi$E1 beam line
could deliver \sn{}{3} muons/\si{\s} at 1\% momentum spread, and
\sn{}{4} muons/\si{\s} at 3\% momentum spread. The muon stopping distribution
of the muons could be well-identified using this excellent beam.
The principle of the particle identification used in the AlCap experiment is
that for each species, the function describes the relationship between energy
loss per unit length (dE/dx) and the particle energy E is uniquely defined.
With a simple system of two detectors, dE/dx can be obtained by
measuring energy deposit $\Delta$E in one detector of known thickness
$\Delta$x, and E is the sum of energy deposit in both detector if the particle
is fully stopped.
Emitting charged particles from nuclear muon capture will be identified by the
specific energy loss. The specific energy loss is calculated as energy loss
per unit path length \sdEdx at a certain energy $E$. The quantity is uniquely
defined for each particle species.
In the AlCap, we realise the idea with a pair of silicon detectors: one thin
detector of 65~\micron\ serves as the $\Delta$E counter, and one thick detector
of 1500~\micron\ that can fully stop protons up to about 12~MeV. Since the
$\Delta \textrm{d}=65$~\micron\ is known, the function relates dE/dx to
E reduces to a function between $\Delta$E and E. Figure~\ref{fig:pid_sim} shows
that the function of protons can be clearly distinguished from other charged
particles in the energy range of interest.
The specific energy loss is measured in the AlCap using a pair of silicon
detectors: a \SI{65}{\um}-thick detector, and a \SI{1500}{\um}-thick detector.
Each detector is $5\times5$ \si{\cm^2} in area.
The thinner one provides $\mathop{dE}$ information, while the sum energy
deposition in the two gives $E$, if the particle is fully stopped. The silicon
detectors pair could help distinguish protons from other charged particles from
\SIrange{2.5}{12}{\MeV} as shown in \cref{fig:pid_sim}.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.75\textwidth]{figs/pid_sim}
\caption{Simulation study of PID using a pair of silicon detectors}
\caption{Simulation study of PID using a pair of silicon detectors. The
detector resolutions follow the calibration results provided by the
manufacturer.}
\label{fig:pid_sim}
\end{figure}
The AlCap uses two pairs of detector with large area, placed symmetrically with
respect to the target provide a mean to check for muon stopping distribution.
The absolute number of stopped muons are inferred
Two pairs of detectors, placed symmetrically with
respect to the target, provide a mean to check for muon stopping distribution
inside the target. The absolute number of stopped muons is calculated
from the number of muonic X-rays recorded by a germanium detector. For
aluminium, the $(2p-1s)$ line is at 346 \kilo\electronvolt. The acceptances of
aluminium, the $(2p-1s)$ line is at \SI{346.828}{\keV}. The acceptances of
detectors will be assessed by detailed Monte Carlo study using Geant4.
% subsection experimental_method (end)
@@ -855,7 +854,7 @@ 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 2.5 MeV.
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
@@ -884,7 +883,7 @@ than 1 MeV up to 10 MeV. \\
\end{itemize}
WP1 is the most developed
project in this program. Most of the associated apparatus has been built and
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.

3
thesis/custom_macro.tex
View File

@@ -50,6 +50,9 @@ $\mu^- \rightarrow e^- \nu_\mu \overline{\nu}_e e^+ e^-$\xspace
\newcommand{\cc}{$c$\xspace}
\newcommand{\dEdx}{$\dfrac{\mathop{dE}}{\mathop{dx}}$\xspace}
\newcommand{\sdEdx}{$\sfrac{\mathop{dE}}{\mathop{dx}}$\xspace}
\newcommand{\rootana}{{\ttfamily rootana}}
\newcommand{\alcapana}{{\ttfamily alcapana}}
\newcommand{\tpulseisland}{{\ttfamily TPulseIsland}}

4
thesis/thesis.tex
View File

@@ -32,8 +32,8 @@ for the COMET experiment}
%\input{chapters/chap1_intro}
%\input{chapters/chap2_mu_e_conv}
%\input{chapters/chap3_comet}
%\input{chapters/chap4_alcap_phys}
%\input{chapters/chap5_alcap_setup}
\input{chapters/chap4_alcap_phys}
\input{chapters/chap5_alcap_setup}
\input{chapters/chap6_analysis}
%\input{chapters/chap7_results}