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chap5, chap6 work with siunitx

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2014-09-10 16:01:53 +09:00
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thesis/chapters/chap6_analysis.tex
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@@ -4,7 +4,7 @@
\section{Analysis modules}
\label{sec:analysis_modules}
A full analysis has not been completed yet, but initial analysis
based on the existing modules (Table~\ref{tab:offline_modules}) is possible
based on the existing modules (\cref{tab:offline_modules}) is possible
thanks to the modularity of the analysis framework.
\begin{table}[htb]
@@ -30,16 +30,16 @@ thanks to the modularity of the analysis framework.
\end{table}
The MakeAnalysedPulses module takes a raw waveform, calculates the pedestal
from a predefined number of first samples, subtracts this pedestal, takes
from a predefined number of first samples, subtracts this pedestal taking
pulse polarity into account, then calls another module to extract pulse
parameters. At the moment, the simplest module, so-called MaxBinAPGenerator,
for pulse information calculation is in use. The module looks for the
sample that
has the maximal deviation from the baseline, takes the deviation as pulse
amplitude and the time stamp of the sample as pulse time. The procedure is
illustrated on Figure~\ref{fig:tap_maxbin_algo}. This module could not detect
illustrated on \cref{fig:tap_maxbin_algo}. This module could not detect
pile up or double pulses in one \tpulseisland{} in
Figure~\ref{fig:tap_maxbin_bad}.
\cref{fig:tap_maxbin_bad}.
\begin{figure}[htb]
\centering
\includegraphics[width=0.85\textwidth]{figs/tap_maxbin_algo}
@@ -82,7 +82,7 @@ the beam rate was generally less than \SI{8}{\kilo\hertz}.
%candidate: a prompt hit on the target in $\pm 200$ \si{\nano\second}\ around the
%time of the $\mu$Sc pulse. The number comes from the observation of the
%time correlation between hits on the target and the $\mu$Sc
%(Figure~\ref{fig:tme_sir_prompt_rational}).
%(\cref{fig:tme_sir_prompt_rational}).
%\begin{figure}[htb]
%\centering
%\includegraphics[width=0.85\textwidth]{figs/tme_sir_prompt_rational}
@@ -97,7 +97,7 @@ rate, time correlation to hits on $\mu$Sc, \ldots on each channel during the
data collecting period. Runs with significant difference from the nominal
values were further checked for possible causes, and would be discarded if such
discrepancy was too large or unaccounted for. Examples of such trend plots are
shown in Figure~\ref{fig:lldq}.
shown in \cref{fig:lldq}.
\begin{figure}[htb]
\centering
\includegraphics[width=0.47\textwidth]{figs/lldq_noise}
@@ -131,15 +131,10 @@ During data taking period, electrons in the beam were were also used for energy
calibration of thick silicon detectors where energy deposition is large enough.
The muons at different momenta provided another mean of calibration in the beam
tuning period.
%Typical pulse height spectra of the silicon detectors are shown
%in Figure~\ref{fig:si_eg_spectra}.
According to Micron Semiconductor
\footnote{\url{http://www.micronsemiconductor.co.uk/}}, the
manufacturer of the silicon detectors, the nominal thickness of the dead layer on
each side is 0.5~\si{\micro\meter}. The alpha particles from the source would deposit
about 66~keV in this layer, and the peak would appear at 5418~keV
(Figure~\ref{fig:toyMC_alpha}).
The alpha particles from the source would deposit
about 66~keV in the \SI{0.5}{\micro\meter}-thick dead layer, and the peak would
appear at 5418~keV (\cref{fig:toyMC_alpha}).
\begin{figure}[htb]
\centering
\includegraphics[width=0.6\textwidth]{figs/toyMC_alpha}
@@ -149,7 +144,7 @@ about 66~keV in this layer, and the peak would appear at 5418~keV
\end{figure}
The calibration coefficients for the silicon channels are listed in
Table~\ref{tab:cal_coeff}.
\cref{tab:cal_coeff}.
\begin{table}[htb]
\begin{center}
\begin{tabular}{l c r}
@@ -183,7 +178,7 @@ source\footnote{Energies and intensities of gamma rays are taken from the
X-ray and Gamma-ray Decay Data Standards for Detector Calibration and Other
Applications, which is published by IAEA at \\
\url{https://www-nds.iaea.org/xgamma_standards/}}, the
recorded pulse height spectrum is shown in Figure~\ref{fig:ge_eu152_spec}. The
recorded pulse height spectrum is shown in \cref{fig:ge_eu152_spec}. The
source was placed at the target position so that the absolute efficiencies can
be calibrated. The relation between pulse height in ADC count and energy is
found to be:
@@ -197,7 +192,7 @@ worse at 3.1~\si{\kilo\electronvolt}~for the annihilation photons at
The absolute efficiencies for the $(2p-1s)$ lines of aluminium
(346.828~\si{\kilo\electronvolt}) and silicon (400.177~\si{\kilo\electronvolt}) are
presented in Table~\ref{tab:xray_eff}. In the process of efficiency calibration,
presented in \cref{tab:xray_eff}. In the process of efficiency calibration,
corrections for true coincidence summing and self-absorption were not applied.
The true coincidence summing probability is estimated to be very
small, about \sn{5.4}{-6}, thanks to the far geometry of the calibration. The
@@ -263,7 +258,7 @@ polyethylene is less than \sn{4}{-4} for a 100~\si{\kilo\electronvolt}\ photon.
%detector was placed perpendicular to the nominal beam path, after an oval
%collimator. The beam momentum scaling factor was scanned from 1.10 to 1.60,
%muon momenta and energies in the measured points are listed in
%Table~\ref{tab:mu_scales}.
%\cref{tab:mu_scales}.
%\begin{table}[htbp]
%\begin{center}
%\begin{tabular}{c c c c}
@@ -301,7 +296,7 @@ polyethylene is less than \sn{4}{-4} for a 100~\si{\kilo\electronvolt}\ photon.
\label{sec:charged_particles_from_muon_capture_on_silicon_thick_silicon}
This analysis was done on a subset of the active target runs 2119 -- 2140
because of the problem of wrong clock frequency found in the data quality
checking shown in Figure~\ref{fig:lldq}. The data set contains \sn{6.43}{7}
checking shown in \cref{fig:lldq}. The data set contains \sn{6.43}{7}
muon events.
%64293720
@@ -316,7 +311,7 @@ Because of the active target, a stopped muon would cause two coincident hits on
the muon counter and the target. The energy of the muon hit on the active
target is also well-defined as a narrow momentum spread beam was used. The
correlation between the energy and timing of all the hits on the active target
is shown in Figure~\ref{fig:sir2f_Et_corr}. The most intense spot at zero time
is shown in \cref{fig:sir2f_Et_corr}. The most intense spot at zero time
and about 5 MeV energy corresponds to stopped muons in the thick target. The
band below 1 MeV is due to electrons, either in the beam or from muon decay in
orbits, or emitted during the cascading of muon to the muonic 1S state. The
@@ -341,7 +336,7 @@ particles from the stopped muons:
It can be seen that there is a faint stripe of muons in the time larger than
1200~ns region, they are scattered muons by other materials without hitting the
muon counter. The electrons in the beam caused the constant band below 1 MeV and
$t > 5000$ ns (see Figure~\ref{fig:sir2_1us_slices}).
$t > 5000$ ns (see \cref{fig:sir2_1us_slices}).
\begin{figure}[htb]
\centering
\includegraphics[width=0.85\textwidth]{figs/sir2_sir2f_amp_1us_slices}
@@ -401,8 +396,8 @@ hits:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Number of charged particles with energy above 2~MeV}
\label{sub:number_of_charged_particles_with_energy_from_8_10_mev}
As shown in Figure~\ref{fig:sir2_1us_slices} and illustrated by MC simulation
in Figure~\ref{fig:sir2_mc_pdfs}, there are several components in
As shown in \cref{fig:sir2_1us_slices} and illustrated by MC simulation
in \cref{fig:sir2_mc_pdfs}, there are several components in
the energy spectrum recorded by the active target:
\begin{enumerate}
\item charged particles from nuclear muon capture, this is the signal we are
@@ -484,7 +479,7 @@ The number of nuclear captures can be inferred from the number of recorded
muonic X-rays. The reference values of the parameters needed for the
calculation taken from Suzuki et al.~\cite{SuzukiMeasday.etal.1987} and Measday
et al.~\cite{MeasdayStocki.etal.2007} are
listed in Table~\ref{tab:mucap_pars}.
listed in \cref{tab:mucap_pars}.
\begin{table}[htb]
\begin{center}
\begin{tabular}{l l l}
@@ -505,7 +500,7 @@ listed in Table~\ref{tab:mucap_pars}.
\end{table}
The muonic X-ray spectrum emitted from the active target is shown in
Figure~\ref{fig:sir2_xray}. The $(2p-1s)$ line is seen at
\cref{fig:sir2_xray}. The $(2p-1s)$ line is seen at
399.5~\si{\kilo\electronvolt}, 0.7~\si{\kilo\electronvolt}\ off from the
reference value of 400.177~\si{\kilo\electronvolt}. This discrepancy is within our
detector's resolution, and the calculated efficiency is
@@ -552,7 +547,7 @@ corrected for several effects:
pulse time, and (b) the reset pulses of the transistor reset preamplifier.
The effects of the two dead time could be calculated by examining the
interval between two consecutive pulses on the germanium detector in
Figure~\ref{fig:sir2_ge_deadtime}.
\cref{fig:sir2_ge_deadtime}.
\begin{figure}[htb]
\centering
\includegraphics[width=0.85\textwidth]{figs/sir2_ges_self_tdiff}
@@ -592,7 +587,7 @@ corrected for several effects:
\end{itemize}
The number of X-rays after applying all above corrections is 3293.5. The X-ray
intensity in Table~\ref{tab:mucap_pars} was normalised to the number of stopped
intensity in \cref{tab:mucap_pars} was normalised to the number of stopped
muons, so the number of stopped muons is:
\begin{align}
@@ -602,9 +597,9 @@ muons, so the number of stopped muons is:
&= 9.03\times10^6 \nonumber
\end{align}
where $\epsilon_{(2p-1s)}$ is the calibrated absolute efficiency of the
detector for the 400.177~keV line in Table~\ref{tab:xray_eff}, and
detector for the 400.177~keV line in \cref{tab:xray_eff}, and
$I_{(2p-1s)}$ is the probability of emitting this X-ray per stopped muon
(80.3\% from Table~\ref{tab:mucap_pars}).
(80.3\% from \cref{tab:mucap_pars}).
Taking the statistical uncertainty of the peak area, and systematic
uncertainties from parameters of muon capture, the number of stopped muons
@@ -621,7 +616,7 @@ The number of nuclear captured muons is:
\label{eqn:sir2_Ncapture}
\end{equation}
where the $f_{\textrm{cap.Si}}$ is the probability of nuclear capture per
stopped muon from Table~\ref{tab:mucap_pars}.
stopped muon from \cref{tab:mucap_pars}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Emission rate of charged particles}
\label{sub:emission_rate_of_charged_particles}
@@ -633,7 +628,7 @@ nuclear muon capture in~\eqref{eqn:sir2_Ncapture}:
= \frac{149.9\times10^4}{7.25\times10^6} = 0.252
\end{equation}
Uncertainties of this rate calculation are listed in
Table~\ref{tab:sir2_uncertainties}, including:
\cref{tab:sir2_uncertainties}, including:
\begin{itemize}
\item uncertainties from number of charged particles, both statistical and
systematic (from spectrum shape and fitting) ones are absorbed in the
@@ -690,7 +685,7 @@ So, the emission rate is:
%\label{fig:sobottka_spec}
%\end{figure}
%The spectrum measured by Sobottka and Wills~\cite{SobottkaWills.1968} is
%reproduced in Figure~\ref{fig:sobottka_spec}, the spectral integral in the
%reproduced in \cref{fig:sobottka_spec}, the spectral integral in the
%energy region from 8 to 10~\si{\mega\electronvolt}\ is $2086.8 \pm 45.7$.
%The authors obtained the spectrum in a 4~\si{\micro\second}\ gate period which began
%1~\si{\micro\second}\ after a muon stopped, which would take 26.59\% of the emitted
@@ -769,11 +764,11 @@ within a coincidence window of $\pm 0.5$~\si{\micro\second}\ around the thick
silicon hit, the two hits are considered to belong to one particle with
$\Delta$E being the energy of the thin hit, and total E being the sum energy of
the two hits. Particle identification is done using correlation between
$\Delta$E and E. Figure~\ref{fig:si16p_dedx_nocut} shows clearly visible banding
$\Delta$E and E. \cref{fig:si16p_dedx_nocut} shows clearly visible banding
structure. No cut on energy deposit or timing with respect to muon hit are
applied yet.
With the aid from MC study (Figure~\ref{fig:pid_sim}), the banding on the
With the aid from MC study (\cref{fig:pid_sim}), the banding on the
$\Delta$E-E plots can be identified as follows:
\begin{itemize}
\item the densest spot at the lower left conner belonged to electron hits;
@@ -804,13 +799,13 @@ $\Delta$E-E plots can be identified as follows:
\end{figure}
It is observed that the banding is more clearly visible in a log-log scale
plots like in Figure~\ref{fig:si16p_dedx_cut_explain}, this suggests
plots like in \cref{fig:si16p_dedx_cut_explain}, this suggests
a geometrical cut on the logarithmic scale would be able to discriminate
protons from other particles. The protons and deuterons bands are nearly
parallel to the $\ln(\Delta \textrm{E [keV]}) + \ln(\textrm{E [keV]})$ line,
but have a slightly altered slope because $\ln(\textrm{E})$ is always greater
than $\ln(\Delta\textrm{E})$. The two parallel lines on
Figure~\ref{fig:si16p_dedx_cut_explain} suggest a check of
\cref{fig:si16p_dedx_cut_explain} suggest a check of
$\ln(\textrm{E}) + 0.85\times\ln(\Delta \textrm{E})$ could tell
protons from other particles.
@@ -829,11 +824,11 @@ $\ln(\textrm{E}) < 9$, which corresponds to $\textrm{E} < 8$~MeV.
The cut of $\ln(\textrm{E}) < 9$ is applied first, then
$\ln(\textrm{E})+ 0.85\times\ln(\Delta \textrm{E}) $ is plotted as
Figure~\ref{fig:si16p_loge+logde}. The protons make a clear peak in the region
\cref{fig:si16p_loge+logde}. The protons make a clear peak in the region
between 14 and 14.8, the next peak at 15 corresponds to deuteron.
Imposing the
$14<\ln(\textrm{E})+ 0.85\times\ln(\Delta \textrm{E})<14.8$ cut,
the remaining proton band is shown on Figure~\ref{fig:si16p_proton_after_ecut}.
the remaining proton band is shown on \cref{fig:si16p_proton_after_ecut}.
\begin{figure}[htb]
\centering
@@ -854,7 +849,7 @@ the remaining proton band is shown on Figure~\ref{fig:si16p_proton_after_ecut}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Number of muon captures}
\label{sub:number_stopped_muons}
The X-ray spectrum from this silicon target on Figure~\ref{fig:si16_xray} is
The X-ray spectrum from this silicon target on \cref{fig:si16_xray} is
significantly noisier than the previous data set of SiR2, suffers from both
lower statistics and a more relaxed muon definition. The peak of $(2p-1s)$
X-ray at 400.177~keV can still be recognised but on a very high background. The
@@ -881,7 +876,7 @@ reducing the background level under the 400.177 keV peak by about one third.
Using the same procedure on the region from 396 to 402 keV (without
self-absorption correction since this is a thin target), the number of
X-rays recorded and the number of captures are shown in
Table~\ref{tab:si16p_ncapture_cal}.
\cref{tab:si16p_ncapture_cal}.
\begin{table}[htb]
\begin{center}
\begin{tabular}{l l c c c}
@@ -920,8 +915,8 @@ Table~\ref{tab:si16p_ncapture_cal}.
To check the origin of the protons recorded, lifetime measurements were made by
cutting on time difference between a hit on one thick silicon and the muon
hit. Applying the time cut in 0.5~\si{\micro\second}\ time steps on the proton
events in Figure~\ref{fig:si16p_proton_after_ecut}, the number of surviving
protons on each arm are plotted on Figure~\ref{fig:si16p_proton_lifetime}. The
events in \cref{fig:si16p_proton_after_ecut}, the number of surviving
protons on each arm are plotted on \cref{fig:si16p_proton_lifetime}. The
curves show decay constants of $762.9 \pm 13.7$~\si{\nano\second}\ and $754.6 \pm
11.9$,
which are consistent with the each other, and with mean life time of muons in
@@ -939,7 +934,7 @@ The fits are consistent with lifetime of muons in silicon in from after 500~ns,
before that, the time constants are shorter ($655.9\pm 9.9$ and $731.1\pm8.9$)
indicates the contamination from muon captured on material with higher $Z$.
Therefore a timing cut from 500~ns is used to select good silicon events, the
remaining protons are shown in Figure~\ref{fig:si16p_proton_ecut_500nstcut}.
remaining protons are shown in \cref{fig:si16p_proton_ecut_500nstcut}.
The spectra have a low energy cut off at 2.5~MeV because protons with energy
lower than that could not pass through the thin silicon to make the cuts as the
range of 2.5~MeV protons in silicon is about 68~\si{\micro\meter}.
@@ -954,7 +949,7 @@ range of 2.5~MeV protons in silicon is about 68~\si{\micro\meter}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Proton emission rate from the silicon target}
\label{sub:proton_emission_rate_from_the_silicon_target}
The number of protons in Figure~\ref{fig:si16p_proton_ecut_500nstcut} is
The number of protons in \cref{fig:si16p_proton_ecut_500nstcut} is
counted from 500~ns after the muon event, where the survival rate is
$e^{-500/758} = 0.517$.
@@ -974,7 +969,7 @@ The emission rate per muon capture is:
&= \dfrac{2.625 \times 10^5}{6.256\times10^6} \nonumber\\
&= 4.20\times10^{-2}\nonumber
\end{align}
The proton spectra on the Figure~\ref{fig:si16p_proton_ecut_500nstcut} and the
The proton spectra on the \cref{fig:si16p_proton_ecut_500nstcut} and the
emission rate are only effective ones, since the energy of protons are modified
by energy loss in the target, and low energy protons could not escape the
target. Therefore further corrections are needed for both rate and spectrum of
@@ -989,11 +984,11 @@ The uncertainty of the emission rate could come from several sources:
background under the X-ray peak (5.5\%) and the efficiency calibration
\item number of protons: efficiency of the cuts in energy, impacts of the
timing resolution on timing cut. The energy cuts' contribution should be
small since it can be seen from Figure~\ref{fig:si16p_loge+logde}, the peak
small since it can be seen from \cref{fig:si16p_loge+logde}, the peak
of protons is strong and well separated from others. The uncertainty in
timing contribution is significant because all the timing done in this
analysis was on the peak of the slow signals. As it is clear from the
Figure~\ref{fig:tme_sir_prompt_rational}, the timing resolution of the
\cref{fig:tme_sir_prompt_rational}, the timing resolution of the
silicon detector could not be better than 100~ns. Putting $\pm100$~ns into
the timing cut could change the survival rate of proton by about
$1-e^{-100/758} \simeq 13\%$. Also, the low statistics contributes a few
@@ -1024,7 +1019,7 @@ By using only the lower limit on
$\ln(\textrm{E}) + 0.85\times\ln(\Delta \textrm{E})$, the heavy charged
particles can be selected. These particles also show a lifetime that is
consistent with that of muons in silicon
(Figure~\ref{fig:si16p_allparticle_lifetime}).
(\cref{fig:si16p_allparticle_lifetime}).
\begin{figure}[htb]
\centering
\includegraphics[width=0.85\textwidth]{figs/si16p_allparticle_lifetime}
@@ -1041,7 +1036,7 @@ The ratio between the number of protons and other particles at 500~ns is $(1927
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Rate and spectrum correction}
%\label{sub:proton_spectrum_deconvolution}
%The proton spectra on the Figure~\ref{fig:si16p_proton_ecut_500nstcut} and the
%The proton spectra on the \cref{fig:si16p_proton_ecut_500nstcut} and the
%emission rate are only effective ones, since the energy of protons are modified
%by energy loss in the target, and low energy protons could not escape the
%target. Therefore corrections are needed for both rate and spectrum of protons.
@@ -1054,7 +1049,7 @@ The ratio between the number of protons and other particles at 500~ns is $(1927
%The initial spatial distribution of protons is inferred from the muon beam
%momentum using Monte Carlo simulation, and available measured data in momentum
%scanning runs. The response function for this thin silicon target is shown in
%Figure~\ref{fig:si16p_toyMC}.
%\cref{fig:si16p_toyMC}.
%\begin{figure}[htb]
%\centering
%\includegraphics[width=0.85\textwidth]{figs/si16p_toyMC}
@@ -1069,7 +1064,7 @@ The ratio between the number of protons and other particles at 500~ns is $(1927
%The Bayesian method is chosen because it tends to be fast, typical number of
%iterations is from 4--8.
%Figure~\ref{fig:si16p_unfold_train} presented results of two tests unfolding with
%\cref{fig:si16p_unfold_train} presented results of two tests unfolding with
%two distributions of initial energy, a Gaussian distribution and
%a parameterized function in~\eqref{eqn:EH_pdf}. The numbers of protons obtained
%from the tests show agreement with the generated numbers.
@@ -1084,8 +1079,8 @@ The ratio between the number of protons and other particles at 500~ns is $(1927
%\end{figure}
%Finally, the unfolding is applied on the spectra in
%Figure~\ref{si16p_proton_spec}, the results are shown in
%Figure~\ref{si16p_unfold_meas}.
%\cref{si16p_proton_spec}, the results are shown in
%\cref{si16p_unfold_meas}.
%\begin{figure}[htb]
%\centering
%\includegraphics[width=0.85\textwidth]{figs/si16p_unfold_meas}
@@ -1127,7 +1122,7 @@ passive silicon runs were applied.
\subsection{The number of stopped muons}
\label{sub:the_number_of_stopped_muons}
The X-ray spectrum on the germanium detector is shown on
Figure~\ref{fig:al100_ge_spec}.
\cref{fig:al100_ge_spec}.
\begin{figure}[htb]
\centering
\includegraphics[width=0.85\textwidth]{figs/al100_ge_spec}
@@ -1153,7 +1148,7 @@ target are:
\label{sub:particle_identification}
Using the same charged particle selection
procedure and the cuts on $\ln(\textrm{E})$ and $\ln(\Delta\textrm{E})$, the
proton energy spectrum is shown in Figure~\ref{fig:al100_proton_spec}.
proton energy spectrum is shown in \cref{fig:al100_proton_spec}.
\begin{figure}[htb]
\centering
\includegraphics[width=1\textwidth]{figs/al100_selection}
@@ -1163,13 +1158,13 @@ proton energy spectrum is shown in Figure~\ref{fig:al100_proton_spec}.
\end{figure}
The lifetime of these protons are shown in
Figure~\ref{fig:al100_proton_lifetime}, the fitted decay constant on the right
\cref{fig:al100_proton_lifetime}, the fitted decay constant on the right
arm is consistent with the reference value of $864 \pm 2$~\si{\nano\second}~\cite{}.
But the left arm gives $918 \pm 16.1$~\si{\nano\second}, significantly larger than
the reference value.
%The longer lifetime suggested some contributions from
%other lighter materials, one possible source is from muons captured on the back
%side of the collimator (Figure~\ref{fig:alcap_setup_detailed}).
%side of the collimator (\cref{fig:alcap_setup_detailed}).
%For this reason, the emission rate calculated from the left arm will be taken as upper
%limit only.
\begin{figure}[htb]
@@ -1185,7 +1180,7 @@ and the decay constant on the SiL1-1 alone was nearly about 1000~\si{\micro\seco
The reason for this behaviour is not known yet. For this emission rate
calculation, this channel is discarded and the rate on the left arm is scaled
with a factor of 4/3. The proton spectrum from the aluminium target is plotted
on Figure~\ref{fig:al100_proton_spec_wosil11}.
on \cref{fig:al100_proton_spec_wosil11}.
\begin{figure}[htb]
\centering