accelerator lab work

accelerator/report/report.tex

@@ -29,7 +29,7 @@
 
 
 \title{Lab 4: Nuclear Reactions and Nucleosynthesis}
-\author{Otho Ulrich, Eugene Kopf, Asghar Kayani, Mike Pirkola, Jacob, }
+\author{Otho Ulrich, Eugene Kopf, Mike Pirkola, Jacob Burke, Andrew Messecar, Spencer Henning, Asghar Kayani}
 \maketitle
 
 \begin{abstract}
@@ -57,7 +57,7 @@ A 2 MeV proton beam is used to annihilate lithium and flourine atoms from a LiF
 
 \section{Proton Beam and Detector}
     \label{sec:detector}
-    The Tandem Van de Graff Accelerator Lab provided a $1.95\pm0.05$ MeV proton beam incident on a LiF foil. Under these conditions, we expected the nuclear reactions described in Section~\ref{sec:reactions} to occur, and Rutherford scattering. We used a circular normal-faced surface barrier detector to observe the alpha particle products of \FpaO\ and \LipaHe\ and the protons from Rutherford scattering. \cite{ADVLABACCEL} The detector was positioned at $149.95\degree\pm0.05\degree$ from the proton beam, which we define as the lab frame of reference; see Figure~\ref{fig:detector}.
+    The Tandem Van de Graff Accelerator Lab provided a $1.95\pm0.05$ MeV proton beam for three experiments. When incident on a lithium-fluoride foil, we expect the nuclear reactions described in Section~\ref{sec:reactions} to occur. When the beam is incident on a silicon or copper foil, we expect Rutherford scattering. We used a circular normal-faced surface barrier detector to observe the alpha particle products of \FpaO\ and \LipaHe\ and the protons from Rutherford scattering. \cite{ADVLABACCEL} The detector was positioned at $149.95\degree\pm0.05\degree$ from the proton beam, which we define as the lab frame of reference; see figure~\ref{fig:detector}.
 
     \begin{figure}
         \center
@@ -67,7 +67,7 @@ A 2 MeV proton beam is used to annihilate lithium and flourine atoms from a LiF
         \label{fig:detector}
     \end{figure}
     
-    The end goal is to create an alpha particle spectrum, and toward this the detector is used to count alpha particles and measure their kinetic energy. An alpha particle incident on the detector creates a current pulse which is converted to a voltage pulse with a high-impendence conductor. The voltage signal is then sent by way of a pre-amplifier to the receiving amplifier in the control room. A multi-channel analyzer receives voltage signals from the second amplifier, binning counts as a function of voltage. The amplifier is adjustable, allowing the voltage range to fit properly within the MCA's detection domain, and the voltage received at the MCA is directly proportional to the kinetic energy of the alpha particle. \cite{ADVLABACCEL} In Section~\ref{sec:reactions:calibration}, a kinetic energy scale is calibrated to the voltage scale, thus providing the alpha particle spectrum.
+    The measurement apparatus serves to create a kinetic energy spectrum of charged particles. An alpha particle or proton (or any other charged particle) incident on the detector creates a current pulse which is converted to a voltage pulse across a high-impendence conductor. The voltage signal is then sent by way of a pre-amplifier to the receiving amplifier in the control room. A multi-channel analyzer receives voltage signals from the second amplifier, binning counts as a function of voltage. The amplifier is adjustable, allowing the voltage range to fit properly within the MCA's detection domain, and the voltage received at the MCA is directly proportional to the kinetic energy of the alpha particle. \cite{ADVLABACCEL} In Section~\ref{sec:reactions:calibration}, a kinetic energy scale is calibrated to the voltage scale, thus providing the charged-particle spectrum.
 
 
 %─────────────
@@ -75,7 +75,14 @@ A 2 MeV proton beam is used to annihilate lithium and flourine atoms from a LiF
 \section{Nuclear Reactions and Detection Plan}
     \label{sec:reactions}
     
-    The nuclear reactions \FpaO\ and \LipaHe\ can be analyzed in terms of the kinematic diagram in Figure~\ref{fig:kinematics}. In this diagram, each M\#,E\# pair refers to the mass and kinetic energy of a particle involved in the collision, with associations defined in Table~\ref{tab:MEpairs}. In the case where the incident particle does not have sufficient kinetic energy to overcome the electric potential barrier of the target nucleus, Rutherford scattering will occur. When it does overcome the potential barrier, a nuclear reaction may occur. We ignore tunneling in this analysis, which is a potential source of error.
+    The nuclear reactions \FpaO\ and \LipaHe\ can be analyzed in terms of the kinematic diagram in figure~\ref{fig:kinematics}. In this diagram, each M\#,E\# pair refers to the mass and kinetic energy of a particle involved in the collision, with associations defined in table~\ref{tab:MEpairs}. In the case where the incident particle does not have sufficient kinetic energy to overcome the electric potential barrier of the target nucleus, Rutherford scattering will occur. When it does overcome the potential barrier, a nuclear reaction may occur. We ignore tunneling in this analysis, which is a potential source of error.
+
+    \begin{figure}
+        \center
+        \includegraphics[width=4.5in]{collision.png}
+        \caption{In general, an incident particle collides with a target nucleus, resulting in an emitted particle and a residual nucleus. The backscattering experiments in this study have $\theta = 149.95\degree\pm0.05\degree$ \cite{ADVLABACCEL}.}
+        \label{fig:kinematics}
+    \end{figure}
 
     \begin{table}
         \center
@@ -85,35 +92,61 @@ A 2 MeV proton beam is used to annihilate lithium and flourine atoms from a LiF
             M3,E3: & Emitted Particle \\
             M4,E4: & Residual Nucleus \\
         \end{tabular}
-        \caption{These variables represent the mass and kinetic energies of the particles involved in the collision described in Figure~\ref{fig:kinematics}.}
+        \caption{These variables represent the mass and kinetic energies of the particles involved in the collision described in figure~\ref{fig:kinematics}.}
         \label{tab:MEpairs}
     \end{table}
 
-    The particle masses used to predict the nuclear reactions and scattering are tabulated in Table~\ref{tab:masses}. Lithium and fluorine are provided by a LiF foil that is placed across the detector, so the available Lithium is $^7$Li and fluorine $^{19}$F. 
+    \begin{table}
-
+        \center
- 	\begin{table}
+        \begin{tabular}{lrllr}
- 		\center
+            Isotope  &Mass (amu)&Abundance&Kinematic Factor&\\
- 		\begin{tabular}{rl}
+            \hline 
- 			Species	 &	Mass \\
+            p/$^1$H$^+$&1.67262158(13)&&&\cite{Carroll&Ostlie} \\
- 			\hline 
+            $\alpha$/$^4$He$^{++}$&4.001506179127(63)&&&\cite{codatarecommended} \\
- 			$^7$Li 	 &	\\	
+            $^4$He   &4.002603 &1.000 &&\cite{Chuetal} \\
- 			$^19$F 	 &	\\
+            $^7$Li   &7.016004 &&&\cite{Chuetal} \\
- 			Cu 	 	 &	\\
+            $^{16}$O &15.994915&0.9976&&\cite{Chuetal} \\
- 			Si 		 &	\\
+            $^{19}$F &18.998405&&&\cite{Chuetal} \\
- 			p 		 &	\\
+            $^{28}$Si&28.086   &1.0000&0.1808&\cite{tesmer1995handbook} \\
- 			$\alpha$ &	\\
+            $^{63}$Cu&62.930   &0.6917&0.4897&\cite{tesmer1995handbook} \\
- 		\end{tabular}
+            $^{65}$Cu&64.928   &0.3083&0.4975&\cite{tesmer1995handbook} \\
- 		\caption{Masses of particles and nuclei involved in our expected nuclear reactions and Rutherford scattering. The lithium and fluoride species are seen in the LiF foil and are expected to undergo nuclear reactions. Cu and Si are the nuclei involved in Rutherford scattering. p and $\alpha$ refer to a proton and an alpha particle, respectively.}
+        \end{tabular}
- 	\end{table}
+        \caption{Properties of nuclei and particles important in our reactions. Li and F nuclei are constituent to LiF foil and are expected to undergo nuclear reactions, with residual nuclei $^{16}$O and $^4$He. The Cu and Si nuclei are involved in Rutherford scattering. p and $\alpha$ refer to a proton and an alpha particle, respectively. Abundances are relative to unit probability for that species, and kinematic factors are included for target nuclei involved in Rutherford scattering of a proton at $150\degree$. Numbers reported without uncertainty are assumed to have uncertainty $\pm$1 on the most precise digit.}
-
+        \label{tab:nuclei} 
+    \end{table}
 
     \subsection{Calibration with Rutherford Scattering}
         \label{sec:reactions:calibration}
-        The maximum expected kinetic energy resulting in Rutherford scattering can be computed, and by observing this value, the energy scale of the detector can be calibrated. Rutherford scattering can be analyzed in terms of Figure~\ref{fig:kinematics}, where M1 = M3, and M2 = M4. The scattering angle $\theta = 149.95\degree\pm0.05\degree$. If the collision is elastic, the kinetic energy of the scattered Proton $E3 \propto E1$. We define a kinetic factor K as the constant of proportionality. This factor can be computed as \cite{ADVLABACCEL} 
+        The maximum expected kinetic energy resulting in Rutherford scattering can be computed, and by observing this value, the energy scale of the detector can be calibrated. Rutherford scattering can be analyzed in terms of figure~\ref{fig:kinematics}, where M1 = M3, and M2 = M4. The scattering angle $\theta = 149.95\degree\pm0.05\degree$. When we assume the collision is elastic, the kinetic energy of the scattered Proton $E3 \propto E1$. We define a kinematic factor K as the constant of proportionality. This factor can be computed as \cite{ADVLABACCEL} 
 
         \begin{equation}
-         	K = \left(\frac{M1 cos(\theta) + \left(M2^2 - M1^2sin^2(\theta)\right)^{1/2}}{M1 + M2}\right)^2. 
+            K = \left(\frac{M1 cos(\theta) + \left(M2^2 - M1^2sin^2(\theta)\right)^{1/2}}{M1 + M2}\right)^2.
+            \label{eq:kinematicfactor}
          \end{equation}
+         Thus,
+        \begin{equation}
+            E3 = K \times E1.
+            \label{eq:rutherford}
+        \end{equation}
+          
+
+        We observe Rutherford scattering of a proton by copper and silicon atoms by performing two experiments, one where the proton beam is incident on a copper foil, and then a silicon foil. Kinematic factors are tabulated in table~\ref{tab:nuclei}. The proton may deposit energy in the target material, so the elastic case is the maximum energy case. A spectrum of energy from scattered protons should therefore be observed, a sum of approximately Gaussian peaks that drops to noise after this highest-energy peak. The expected peaks are tabulated in table~\ref{tab:predictions}.
+
+        \begin{table}
+            \center
+            \begin{tabular}{rl}
+                Reaction&Energy (MeV) \\
+                \hline
+                $^{28}$Si(p)&0.352$\pm$0.009\\
+                $^{63}$Cu(p)&0.95$\pm$0.02\\
+                $^{65}$Cu(p)&0.97$\pm$0.03\\
+                \FpaO&\\
+                \LipaHe& \\
+
+            \end{tabular}
+            \caption{Expected peaks for nuclear reactions and maximum energy of a Rutherford scattered proton. Rutherford scattering energies are computed using equation~\ref{eq:rutherford} with the kinematic factors from table~\ref{tab:nuclei}. $\theta=149\degree\pm0.05\degree$.}
+            \label{tab:predictions}
+        \end{table}
 
 
 
@@ -121,18 +154,17 @@ A 2 MeV proton beam is used to annihilate lithium and flourine atoms from a LiF
 
 
 
-    \begin{figure}
-        \center
-        \includegraphics[width=4.5in]{collision.png}
-        \caption{In general, an incident particle collides with a target nucleus, resulting in an emitted particle and a residual nucleus. The backscattering experiments in this study have $\theta = 149.95\degree\pm0.05\degree$ \cite{ADVLABACCEL}.}
-        \label{fig:kinematics}
-    \end{figure}
-
 
 %─────────────    
 \section{Results}
     \label{sec:results}
 
+        \begin{figure}
+            \center
+            \includegraphics[width=4.5in]{rutherford.pdf}
+            \caption{Across channels 50 through 205, we observed the signal from Rutherford scattering of protons by copper nuclei (black) and silicon nuclei (red). The maximum count for each is estimated at 17600 and 20000 and drawn with the blue and purple line, respectively.}
+        \end{figure}
+
 
 %─────────────
 \section{Conclusion}

adv_lab.bib

@@ -23,14 +23,24 @@
 
 
 
-
+@book{tesmer1995handbook,
+  title={Handbook of modern ion beam materials analysis},
+  author={Tesmer, J.R. and Nastasi, M.A.},
+  isbn={9781558992542},
+  lccn={95038931},
+  series={Mrs Symposium Proceedings Series},
+  url={https://books.google.com/books?id=-YJUAAAAMAAJ},
+  year={1995},
+  publisher={Materials Research Society}
+}
 
 
 @techreport{ADVLABACCEL,
-  author = {Burns, Clement and Kayani, Asghar},
+  author = {Schaus, Richard H. and Smith, Richard J. and Burns, Clement and Kayani, Asghar},
   title = {Nuclear Reactions},
-  institution = {Western Michigan University},
+  institution = {Montana State University, Western Michigan University},
-  year = {2017},
+  month = {March},
+  year = {2016},
   type = {Lab Guide}
 }
 
@@ -57,10 +67,13 @@
   isbn      = {0-12-173850-7}
 }
 
-
+@ONLINE{codatarecommended,
-
+  author = {Peter J. Mohr and Barry N. Taylor and David B. Newell},
-
+  title = {CODATA recommended values of the fundamental physical constants: Alpha Particle Mass in u},
-
+  month = jun,
+  year = {2015},
+  url = {http://physics.nist.gov/cgi-bin/cuu/Value?malu}
+}