pet corrections

This commit is contained in:
hiro98 2020-01-27 18:25:03 +01:00
parent 794b7fa58f
commit 903b9b33ac
17 changed files with 555 additions and 648 deletions

File diff suppressed because one or more lines are too long

View file

@ -67,10 +67,10 @@
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@ -9810,15 +9428,15 @@
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\pgfpathlineto{\pgfqpoint{3.310694in}{1.845954in}}% \pgfpathlineto{\pgfqpoint{1.889444in}{1.458732in}}%
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\pgfpathlineto{\pgfqpoint{2.255278in}{1.873732in}}% \pgfpathlineto{\pgfqpoint{0.834028in}{1.486510in}}%
\pgfpathquadraticcurveto{\pgfqpoint{2.227500in}{1.873732in}}{\pgfqpoint{2.227500in}{1.845954in}}% \pgfpathquadraticcurveto{\pgfqpoint{0.806250in}{1.486510in}}{\pgfqpoint{0.806250in}{1.458732in}}%
\pgfpathlineto{\pgfqpoint{2.227500in}{0.698177in}}% \pgfpathlineto{\pgfqpoint{0.806250in}{0.698177in}}%
\pgfpathquadraticcurveto{\pgfqpoint{2.227500in}{0.670399in}}{\pgfqpoint{2.255278in}{0.670399in}}% \pgfpathquadraticcurveto{\pgfqpoint{0.806250in}{0.670399in}}{\pgfqpoint{0.834028in}{0.670399in}}%
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@ -9830,15 +9448,15 @@
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\pgfpathlineto{\pgfqpoint{2.560833in}{1.769565in}}% \pgfpathlineto{\pgfqpoint{1.139583in}{1.382343in}}%
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@ -9847,15 +9465,15 @@
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\pgfpathlineto{\pgfqpoint{2.560833in}{1.575954in}}% \pgfpathlineto{\pgfqpoint{1.139583in}{1.188732in}}%
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@ -9865,15 +9483,15 @@
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\pgfpathlineto{\pgfqpoint{2.560833in}{1.382343in}}% \pgfpathlineto{\pgfqpoint{1.139583in}{0.995121in}}%
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@ -9882,50 +9500,15 @@
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Binary file not shown.

View file

@ -2267,3 +2267,315 @@
\label{fig:calibration-comp} \label{fig:calibration-comp}
\end{figure} \end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/mid_over_energy.pgf}
\caption{}
\label{fig:calibration-mid_over_energy}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/mid_over_channel.pgf}
\caption{}
\label{fig:calibration-mid_over_channel}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/time_range.pgf}
\caption{}
\label{fig:calibration-time_range}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/all_times.pgf}
\caption{}
\label{fig:calibration-all_times}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/comp.pgf}
\caption{}
\label{fig:calibration-comp}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf}
\caption{}
\label{fig:calibration-lenght_det}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/tom1/3dplot.pgf}
\caption{}
\label{fig:tom1-3dplot}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/tom1/filtered_fit.pgf}
\caption{}
\label{fig:tom1-filtered_fit}
\end{figure}
\begin{figure}[H]\centering
\input{../auswertung/figs/tom1/unfiltered_fit.pgf}
\caption{}
\label{fig:tom1-unfiltered_fit}
\end{figure}

View file

@ -2,7 +2,7 @@
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@ -34,7 +34,7 @@
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@ -52,7 +52,7 @@
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@ -85,7 +85,7 @@
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@ -115,7 +115,7 @@
}, },
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@ -132,7 +132,7 @@
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] ]
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@ -155,7 +155,7 @@
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@ -183,7 +183,7 @@
}, },
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@ -204,7 +204,7 @@
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@ -221,7 +221,7 @@
"(19.115801602937395, 0.5738039944241058)" "(19.115801602937395, 0.5738039944241058)"
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@ -232,7 +232,7 @@
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"metadata": { "metadata": {
"autoscroll": false, "autoscroll": false,
"collapsed": false, "collapsed": false,
@ -249,7 +249,7 @@
"(19.1, 0.6)" "(19.1, 0.6)"
] ]
}, },
"execution_count": 67, "execution_count": 9,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -260,7 +260,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 68, "execution_count": 10,
"metadata": { "metadata": {
"autoscroll": false, "autoscroll": false,
"collapsed": false, "collapsed": false,
@ -277,7 +277,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 76, "execution_count": 11,
"metadata": { "metadata": {
"autoscroll": false, "autoscroll": false,
"collapsed": false, "collapsed": false,
@ -315,7 +315,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 77, "execution_count": 16,
"metadata": { "metadata": {
"autoscroll": false, "autoscroll": false,
"collapsed": false, "collapsed": false,

View file

@ -46,6 +46,10 @@ channel_to_time_val = SecondaryValue('a + b*(k-1/2)',
def channel_to_time(channel, d=0): def channel_to_time(channel, d=0):
return channel_to_time_val(k=(channel, d)) return channel_to_time_val(k=(channel, d))
def time_to_channel(time):
a = -.014
b = .0483
return ((time - a)/b).astype(int)
def scientific_round(val, err): def scientific_round(val, err):
"""Scientifically rounds the values to the given errors.""" """Scientifically rounds the values to the given errors."""
@ -160,23 +164,27 @@ def plot_spectrum(counts, offset=1, save=None, **pyplot_args):
# Time of Flight Analysiss # # Time of Flight Analysiss #
############################################################################### ###############################################################################
def gauss(x, a, mu, sigma): def gauss(x, a, mu, sigma, o):
return a*np.exp(-(x-mu)**2/(2*sigma**2)) return a*np.exp(-(x-mu)**2/(2*sigma**2)) + o
def find_and_plot_peak(counts, ax, label): def find_and_plot_peak(counts, ax, label, time_interval=[40, 70]):
channels = np.arange(0, counts.size) + 1 channels = np.arange(0, counts.size) + 1
counts = counts.copy()/counts.max() counts = counts.copy()/counts.max()
times, d_times = channel_to_time(channels) times, d_times = channel_to_time(channels)
interval = time_to_channel(np.array(time_interval))
splot = ax.step(times, counts, label=label, alpha=.4) splot = ax.step(times, counts, label=label, alpha=.4)
opt, cov = curve_fit(gauss, channels, counts, opt, cov = curve_fit(gauss, channels[interval[0]:interval[1]],
p0=(1, counts.argmax(), 100)) counts[interval[0]:interval[1]],
sigma=np.sqrt(counts[interval[0]:interval[1]]),
absolute_sigma=True,
p0=(1, counts.argmax(), 100, .3))
cov = np.sqrt(np.diag(cov)) cov = np.sqrt(np.diag(cov))
gplot = ax.plot(times, gauss(channels,*opt), label=f"Fit {label}", color=splot[0].get_color()) gplot = ax.plot(times, gauss(channels,*opt), label=f"Fit {label}",
color=splot[0].get_color())
ax.axvline(channel_to_time(opt[1])[0], color=gplot[0].get_color()) ax.axvline(channel_to_time(opt[1])[0], color=gplot[0].get_color())
t, dt = channel_to_time(opt[1], opt[2]/10) t, dt = channel_to_time(opt[1], cov[1])
ax.axvspan(t-dt, t+dt, alpha=.2, color=gplot[0].get_color()) ax.axvspan(t-dt, t+dt, alpha=.2, color=gplot[0].get_color())
return channel_to_time(opt[1], opt[2]/10) return t, dt
############################################################################### ###############################################################################

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@ -1,4 +1,5 @@
\documentclass[slug=PET, room=Andreas-Schubert-Bau\,\ 424A, supervisor=Carsten\ Bittrich, coursedate=10.\ 01.\ 2020]{../../Lab_Report_LaTeX/lab_report} \documentclass[slug=PET, room=Andreas-Schubert-Bau\,\ 424A,
supervisor=Carsten\ Bittrich, coursedate=10.\ 01.\ 2020, ngerman]{../../Lab_Report_LaTeX/lab_report}
\title{Postitronenemissionstomographie} \title{Postitronenemissionstomographie}
\author{Oliver Matthes, Valentin Boettcher} \author{Oliver Matthes, Valentin Boettcher}
@ -391,7 +392,7 @@ durch~\eqref{tab:caltime}.
\end{equation} \end{equation}
Die Aktivität der \ce{^22Na} Kalibrierungsprobe ergibt sich mit Die Aktivität der \ce{^22Na} Kalibrierungsprobe ergibt sich mit
\(t=\SI{166492800}{\second},\, t_{1/2} = \SI{2.6027\pm .0010}{a}\) und \(A_0 \(t=\SI{166492800\pm 86400}{\second},\, t_{1/2} = \SI{2.6027\pm .0010}{a}\) und \(A_0
= \SI{1.36}{\mega\becquerel}\) (1.10.2014, Abw. \SI{3}{\percent}). = \SI{1.36}{\mega\becquerel}\) (1.10.2014, Abw. \SI{3}{\percent}).
\begin{equation} \begin{equation}
@ -400,8 +401,7 @@ Die Aktivität der \ce{^22Na} Kalibrierungsprobe ergibt sich mit
\frac{\ln{2}}{t_{1/2}}\cdot A\cdot\Delta A = \SI{.333\pm.010}{\mega\becquerel} \frac{\ln{2}}{t_{1/2}}\cdot A\cdot\Delta A = \SI{.333\pm.010}{\mega\becquerel}
\end{equation} \end{equation}
Die Z\"ahlate der zuf\"alligen Koinzidenzen ergibt sich aus Die Z\"ahlate der zuf\"alligen Koinzidenzen ergibt sich aus~\eqref{eq:zufkoinz}
% \todo{!!!!! GLEICHUNG}
mit der Kantenl\"ange des Detektors mit der Kantenl\"ange des Detektors
\(a=\SI{54}{\milli\meter}\) und dem Detektorabstand \(a=\SI{54}{\milli\meter}\) und dem Detektorabstand
\(D=\SI{386}{\milli\meter}\) sowie \(D=\SI{386}{\milli\meter}\) sowie
@ -475,29 +475,32 @@ redundant) so ergibt sich die doppelte Lichtlaufzeit \(\mathfrak{t}\)
zwischen den Detektoren zwischen den Detektoren
(\(t_0 + \mathfrak{t} - (t_0 - \mathfrak{t}) = 2\mathfrak{t}\)). (\(t_0 + \mathfrak{t} - (t_0 - \mathfrak{t}) = 2\mathfrak{t}\)).
Um die Peakpositionen zu erhalten, wurden Gaußfunktionen \"uber die Um die Peakpositionen zu erhalten, wurden Gaußfunktionen (mit
Zeitspektren gefittet. Als Ma\ss{} f\"ur die Peakbreite und damit die vertikalem offset) \"uber die Zeitspektren im Bereich von
(statistische) Unsicherheit wurde \(1/10\) des \(\sigma\) Parameters \SIrange{40}{60}{\nano\second} (links, mitte) und
der Gaußfunktion genutzt (heuristische Absch\"atzung). Nicht explizit \SIrange{45}{65}{\nano\second} (rechts )gefittet. Die (statistische)
betrachtet werden hier der endliche Quellendurchmesser Unsicherheit wurde aus der Fit unsicherheit f\"ur den Mittelwert
\SI{2.5}{\centi\meter} sowie der Restabstand der Quelle zum Detektor \"bernommen. Nicht explizit betrachtet werden hier der endliche
(kleiner \SI{1}{\centi\meter}). Der Prozess wird Quellendurchmesser \SI{2.5}{\centi\meter} sowie der Restabstand der
Quelle zum Detektor (kleiner \SI{1}{\centi\meter}). Der Prozess wird
in~\ref{fig:calibration-lenght_det} illustriert. in~\ref{fig:calibration-lenght_det} illustriert.
\begin{figure}[htb]\centering \begin{figure}[htb]\centering
\input{../auswertung/figs/calibration/lenght_det.pgf} \input{../auswertung/figs/calibration/lenght_det.pgf}
\caption[Abstandsbestimmung]{Bestimmung der Peakpositionen der Zeitspektren zwecks der \caption[Abstandsbestimmung]{Bestimmung der Peakpositionen der Zeitspektren zwecks der
Berechnung des Detektorabstandes. Die farbigen Intervallmarkierungen Berechnung des Detektorabstandes. Die farbigen Intervallmarkierungen
stellen die gesch\"atzte Abweichung dar.} stellen die Abweichung aus dem Fit dar.}
\label{fig:calibration-lenght_det} \label{fig:calibration-lenght_det}
\end{figure} \end{figure}
Entsprechend ergibt sich dann der Detektorabstand zu: Entsprechend ergibt sich dann der Detektorabstand zu
\begin{align} \begin{align}
\label{eq:abst} \label{eq:abst}
\mathfrak{t} &= \SI{2.2\pm .6}{\nano\second} \\ 2\mathfrak{t} &= \SI{2.0\pm .6}{\nano\second} \\
D &= \frac{\mathfrak{t}}{2c} = \SI{330\pm 90}{\milli\meter} D &= \mathfrak{t}\cdot c = \SI{310\pm 90}{\milli\meter}.
\end{align} \end{align}
Dieses Ergebnis ist kompatibel mit dem Litertaturwert von
\SI{386}{\milli\meter}.
\subsubsection{Schwerpunktsdiagramme} \subsubsection{Schwerpunktsdiagramme}
\label{sec:schwpkt} \label{sec:schwpkt}
@ -798,7 +801,7 @@ Ort liegt weit \"uber der mittleren Diffusionsl\"ange der Positronen
Analog zu~\eqref{eq:acttoday} ergibt sich f\"ur die Aktivität der Analog zu~\eqref{eq:acttoday} ergibt sich f\"ur die Aktivität der
\ce{^22Na} Quelle zu Peak 3 mit \ce{^22Na} Quelle zu Peak 3 mit
\(t=\SI{313632000}{\second},\, t_{1/2} = \SI{2.6027\pm .0010}{a}\) \(t=\SI{313632000\pm 86400}{\second},\, t_{1/2} = \SI{2.6027\pm .0010}{a}\)
und \(A_0 = \SI{270}{\kilo\becquerel}\) (1.2.2010, und \(A_0 = \SI{270}{\kilo\becquerel}\) (1.2.2010,
Abw. \SI{3}{\percent}). Abw. \SI{3}{\percent}).
@ -811,8 +814,7 @@ Damit berechnen sich die in~\ref{tab:peakactivities} aufgelisteten
Aktivit\"aten der beiden anderen Proben wie folgt durch Aktivit\"aten der beiden anderen Proben wie folgt durch
Verh\"altnisbildung der Peakvolumina (\(= 2\pi A\sigma**2\)), die ein Verh\"altnisbildung der Peakvolumina (\(= 2\pi A\sigma**2\)), die ein
Ma\ss{} f\"ur die Z\"ahlrate geben. Die Abweichungen liegen alle in Ma\ss{} f\"ur die Z\"ahlrate geben. Die Abweichungen liegen alle in
der Gr\"o\ss{}enordnung von \SI{3}{\percent} und r\"uhren der Gr\"o\ss{}enordnung von \SI{3}{\percent}.
haupts\"achlich von der Abweichung der Aktivit\"at \(A_3\) her.
\begin{equation} \begin{equation}
\label{eq:relakt} \label{eq:relakt}