LB Thesis Post Defense - Revision history

Brenleyt at 20:56, 2 October 2018

2018-10-02T20:56:58Z

Brenleyt at 20:56, 2 October 2018

2018-10-02T20:56:40Z

Show changes

Foretony: /* New SNR Section (8/18) */

2018-09-21T18:14:37Z

New SNR Section (8/18)

Foretony: /* Conclusion */

2018-09-21T18:07:21Z

Conclusion

Brenleyt: /* Appendix A */

2018-08-31T20:45:52Z

Appendix A

Brenleyt: /* Data Analysis */

2018-08-31T20:43:11Z

Data Analysis

Brenleyt: /* Data Analysis */

2018-08-31T20:20:16Z

Data Analysis

Brenleyt: /* Data Analysis */

2018-08-31T20:14:52Z

Data Analysis

Brenleyt: /* Experimental Setup */

2018-08-31T20:08:56Z

Experimental Setup

Brenleyt at 20:07, 31 August 2018

2018-08-31T20:07:21Z

← Older revision		Revision as of 20:56, 2 October 2018
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	This is a recent copy of my thesis to be workshopped.		This is a recent copy of my thesis to be workshopped.
		+	=Old Thesis=

	==Introduction==		==Introduction==

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 \section{Signal to Noise Ratio Calculations}
-\hspace{0.5in} Finding the correct value for the signal to noise ratio was done in three steps. Due to the fact that the specific activities were not all the same for the different normalization reference materials (in this case, the pure Se witness pellet), the first step was to take the weighted average of the specific activities and get normalization factors to force the specific activities to agree with the weighted average. The second step was to construct plots of $\frac{A_{Se Mix}}{a_{Se Pure}}$ to find the conccentration of Se that would need to be removed to have an activity of zero Hz at zero percent concentration of Se. Finally, $\frac{N}{B}$ was plotted as a function of the amount of Se spikant added plus the initial amount of Se that was present in the soil to begin with.
+\hspace{0.5in} Finding the correct value for the signal to noise ratio was done in three steps. Due to the fact that the specific activities were not all the same for the different normalization reference materials (in this case, the pure Se witness pellet), the first step was to take the weighted average of the specific activities and get normalization factors to force the specific activities to agree with the weighted average. The second step was to construct plots of $\frac{A_{Se Mix}}{a_{Se Pure}}$ to find the concentration of Se that would need to be removed to have an activity of zero Hz at zero percent concentration of Se. Finally, $\frac{N}{B}$ was plotted as a function of the amount of Se spikant added plus the initial amount of Se that was present in the soil to begin with.  The minimum detectable limit was defined as being the Se concentration that is two standard deviations from origin where the standard deviation is given by the uncertainty in the y-intecept of the fit in Figure XXX.
 \hspace{0.5in} Table \ref{Se-75 Normalization Table} and Table \ref{Se-81m Normalization Table} outlines the normalization corrections that were made to the specific activity of the pure reference Se to force the denominator of $\frac{A_{Mix Se}}{a_{Pure Se}}$ to be the same across the board.
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 \end{table}
-The 50\% sample was not included because the results were not physical. The signal to noise ratio in both cases was lower than the 10\% SNR. Due to the fact that the sample was very small when compared to the volume of the aluminum cylinder it was contained in, the lab technician may have placed the middle of the sample at the center of the beamline instead of the bottom. This would result in the sample not receiving as much flux as if it were correctly on axis. The 0.1\% was not analyzed for the Se-81m sample because the 103 keV line was not visible due to having to wait roughly two hours for the matrix to cool down enough to reach below 20\% dead time.
+The 50\% sample was not included because the results were not physical. The signal to noise ratio in both cases was lower than the 10\% SNR. Due to the fact that the sample was very small when compared to the volume of the aluminum cylinder it was contained in, the lab technician may have placed the middle of the sample at the center of the beamline instead of the bottom. This would result in the sample not receiving as much flux as if it were correctly on axis. The 0.1\% was not analyzed for the Se-81m sample because the 103 keV line was not visible as a result of waiting roughly two hours (two Se-81m half lives) for the matrix to cool down enough to reach a dead time less than 20\%.
 \hspace{0.5in} The next step was to plot the activity ratio as a function of concentration to identify the initial concentration of Se in the soil sample. The negative x-intercept represented this value.

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 \chapter{Conclusion}
-\hspace{0.5in}The purpose of this experiment was to determine the minimum detectable concentration of Se-82 and Se-76 in soil. Photon activation analysis was used to measure this concentration by creating the unstable isotopes of Se-81m and Se-75.  The minimum detectable concentration for Se-81m is (0.13 $\pm$ 0.06)\%, which would be believable as Se-81m energy lines were not visible in the 0.1\% Se/Soil sample. The minimum detectable concentration for Se-75, as measured 56 days after irradiation, was a (0.005 $\pm$ 0.003)\%. The Se-75 signal is still visible in May of 2018.
+\hspace{0.5in}The purpose of this experiment was to determine the minimum detectable concentration of Se-82 and Se-76 in soil. Photon activation analysis was used to measure this concentration by creating the unstable isotopes of Se-81m and Se-75.  The observed minimum detectable concentration for Se-81m was 0.13 $\pm$ 0.06\% $\left ( 1300 \pm$ 600 \frac{\mu g}{g} \right )$, which is consistent with the inability to observe the Se-81m energy lines in the 0.1\% Se/Soil sample. The minimum detectable concentration for Se-75, as measured 56 days after irradiation, was a 0.005 $\pm$ 0.003\% ( 50 $\pm$ 30 $\frac{\mu g}{g}$). The Se-75 signal was still visible as of May of 2018.
 ==Appendix A==

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      \label{Picket Fence}
 \end{figure}
 This can be overcome by simply fitting the energy peak of interest to a Gaussian function, then applying the calibration to the mean of the fit.

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      \label{3 Chan Sample Hist}
 \end{figure}
 The background rate for the pure sample remained relatively constant when compared to the background rate for the mixture. Table \ref{Background Initial Activity} shows the initial activity of the background and the decay constants.
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 \end{figure}
+[[File:LB Thesis 170048 002 Se75 HLPlot.png|200px]]
 \newpage
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 \end{figure}
+[[File:LB Thesis 170049 002 HLPlot Se81m.png|200px]]
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 \end{figure}
+(Should I increase these to 2 standard deviations for Chebychev's Rule?)

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      \label{1 Chan Sample Hist}
 \end{figure}
 Figure \ref{1 Chan Sample Hist} is a histogram that corresponds to the 103 keV Line of Se-81. By looking at the statistics box in the thin window, the total number of counts can be found by the line labeled "Integral". The intrinsic error in the signal was found by expanding the channel axis by half of the standard deviation of the fit on each side to see how the number of counts varied as the size of the window was varied. A sample of a three channel window with counts $I_{Expanded}$ is shown in Figure \ref{3 Chan Sample Hist}. The purpose of the expansion was to see how inclusion of more channels affected the final result.
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      \label{3 Chan Sample Hist}
 \end{figure}
 Unfortunately in this situation the keV resolution is too small, so the window can only be expanded by 1 on both sides. The systematic error in the signal can be estimated by
 \begin{equation}
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      \label{fig:my_label}
 \end{figure}
 To account for the dead time, the total number of entries in the histogram was divided by the run time to get an average count rate. The plot was used to estimate the dead time. Once the dead time has been estimated, the correction is

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    \end{minipage}
 \end{figure}
 Note the different runs are distinct and can be identified as long as one measurement is known. The larger peaks in Figure 3.3 are from the Co-60's 1.173 and 1.332 MeV lines.
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 One would believe that ratio of the activity of the pure sample and the mixture would be unity if the flux through the target was the same. Unfortunately this was not the case, which would imply that the flux through the samples was not the same. An increase in the divergence and attenuation of the beam could also be attributed to the presence of other targets in front of mine. Another source of error was produced by the relative position of the pure outer Selenium and the Selenium within the soil matrix. Since the level of soil varied, it is highly possible that the Selenium within the mixture was higher or lower (relative to the beam axis) than the pure Selenium. This would impact the flux seen by both sets of Selenium.
 \hspace{0.5in}During the HpGe measurement, one source of error could be the presence of lines produced from the soil matrix competing with the characteristic energy lines from Selenium. As a result the measurement would be higher than expected which would impact the number of counts seen within the chosen window width. Another source of error is simply the noise from within the hall. Many sources and samples were brought into and out of the hall which produced more noise to muddle the measurement.
 ==Conclusion==

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      \label{Targ Setup}
 \end{figure}
 \begin{figure}
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 \end{figure}
 \begin{table}[]
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 \hspace{0.5in} The constant fraction discriminator's purpose was to filter unwanted signals created within the HpGe detector's sensitive volume. The CFD duplicated the analog signal, inverted it, and scaled it by a constant value. Once this has been done the duplicate signal is time-delayed by an amount of time that is less than the rise time of the analog signal. The CFD then searched for a zero crossing point. If such a point was found then the signal was allowed to pass through the CFD. If not, then the signal was rejected. For the purpose of this experiment the lower limit setting resulted in measurements of 40 keV photons or lower being rejected.
 \hspace{0.5in} The peak sensing analog to digital converter is a Wilkinson apparatus which operates by opening a gate for a select amount of time. While the gate is open, the conversion takes place. Assuming the gate is open, the analog pulse is sent through a differentiating circuit, which has an output proportional to the rate of change of the signal. Once the circuit finds a maximum, the voltage is held constant by a capacitor. If a larger signal were to appear, then the capacitor would maintain the larger voltage as opposed to the smaller one. A comparitor was used to decide if a higher voltage appeared while the gate was open. After the gate closes, the capacitor discharges and voltage information is assigned a unique numerical channel.
 ==Data Analysis==

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      \label{Sample Gamma Spectrum}
 \end{figure}
 It is easy to see that there could be lines produced by the selenium radioisotopes with competing energy lines produced by the matrix the selenium was within, or from other radioactive materials within the lab.
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      \label{Ni Energy Decay Sample}
 \end{figure}
 \hspace{0.5in} It can be seen above that the activity will decrease as time goes on due to decay. If both the characteristic energy lines of the isotopes and the half life are in agreement with the attributes of the isotope of interest, then the argument vastly strengthens as there aren't many isotopes with similar half lives and energies. Usually these two pieces of information are sufficient to identify an isotope of interest within the irradiated sample. The argument may be strengthened further, for isotopes with several lines, by quantifying the branching ratios for the different energy lines. The activity of the energy lines should match the branching ratio, but an accurate measurement of the detector efficiency needs to be taken for each energy line.