update, still writing

accelerator/report/report.tex

@@ -101,15 +101,19 @@ A 2 MeV proton beam is used to annihilate lithium and flourine atoms from a LiF
         \begin{tabular}{lrllr}
             Isotope  &Mass (amu)&Abundance&Kinematic Factor&\\
             \hline 
-            p/$^1$H$^+$&1.67262158(13)&&&\cite{Carroll&Ostlie} \\
+            p/$^1$H$^+$&1.00727646688(13)&&&\cite{Carroll&Ostlie} \\
             $\alpha$/$^4$He$^{++}$&4.001506179127(63)&&&\cite{codatarecommended} \\
             $^4$He   &4.002603 &1.000 &&\cite{Chuetal} \\
             $^7$Li   &7.016004 &&&\cite{Chuetal} \\
             $^{16}$O &15.994915&0.9976&&\cite{Chuetal} \\
             $^{19}$F &18.998405&&&\cite{Chuetal} \\
-            $^{28}$Si&28.086   &1.0000&0.1808&\cite{tesmer1995handbook} \\
+            % From Kayani?
-            $^{63}$Cu&62.930   &0.6917&0.4897&\cite{tesmer1995handbook} \\
+            %$^{28}$Si&28.086   &1.0000&0.1808&\cite{tesmer1995handbook} \\
-            $^{65}$Cu&64.928   &0.3083&0.4975&\cite{tesmer1995handbook} \\
+            %$^{63}$Cu&62.930   &0.6917&0.4897&\cite{tesmer1995handbook} \\
+            %$^{65}$Cu&64.928   &0.3083&0.4975&\cite{tesmer1995handbook} \\
+            $^{28}$Si&28.086   &1.0000&0.8746&\cite{tesmer1995handbook} \\
+            $^{63}$Cu&62.930   &0.6917&0.9420&\cite{tesmer1995handbook} \\
+            $^{65}$Cu&64.928   &0.3083&0.9437&\cite{tesmer1995handbook} \\
         \end{tabular}
         \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} 
@@ -137,18 +141,56 @@ A 2 MeV proton beam is used to annihilate lithium and flourine atoms from a LiF
             \begin{tabular}{rl}
                 Reaction&Energy (MeV) \\
                 \hline
-                $^{28}$Si(p)&0.352$\pm$0.009\\
+                % From Kayani's(?) kinematic factors
-                $^{63}$Cu(p)&0.95$\pm$0.02\\
+                %$^{28}$Si(p)&0.352$\pm$0.009\\
-                $^{65}$Cu(p)&0.97$\pm$0.03\\
+                %$^{63}$Cu(p)&0.95$\pm$0.02\\
+                %$^{65}$Cu(p)&0.97$\pm$0.03\\
+                $^{28}$Si(p)&1.706$\pm$0.05\\
+                $^{63}$Cu(p)&1.837$\pm$0.05\\
+                $^{65}$Cu(p)&1.840$\pm$0.05\\
                 \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}. $\theta=149\degree\pm0.05\degree$.}
+            \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}.}
             \label{tab:predictions}
         \end{table}
 
 
+    \subsection{Nuclear Reaction Peaks}
+    \label{sec:reactions:peaks}
+        The kinetic energy of the alpha particle products from \FpaO and \LipaHe are characteristic of those reactions. Binding energies of the involved nuclei are significant compared to their rest masses, so the relativistic equivalence must be considered when computing the energy Q released or absorbed during the reaction, \cite{ADVLABACCEL} so
+
+        \begin{equation}
+             Q = \delta(mc^2) = (M1+M2)c^2 - (M3+M4)c^2.
+             \label{eq:Q}
+         \end{equation}
+
+        Given this method of computing Q, non-relativistic conservation of total energy and momentum provide a sufficiently useful expression for the kinetic energy of the alpha particle product E3 as a function of the kinematic quantities described in figure~\ref{fig:kinematics}. \cite{Ziegler_1975} The expectation value of E3 can be computed as 
+
+        \begin{equation}
+            E3^{1/2} = A\pm(A^2+B)^{1/2}, 
+        \end{equation} where
+        \begin{equation}
+            A = [(M1{\times}M3{\times}E1)^{1/2}/(M3+M4)]cos\theta
+        \end{equation} and
+        \begin{equation}
+            B = [M4{\times}Q+E1(M4-M1)]/(M3+M4). \cite{Meisel1996}
+        \end{equation}
+
+        %\begin{equation}
+        %    E3 = \frac{E1 M1 M3}{(M3 + M4)^2}\Bigg\{2cos^2\theta + \frac{M4(M3+M4)}{M1 M3}\left(\frac{Q}{E1} + 1 - \frac{M1}{M3}\right)
+        %\end{equation}
+        %\begin{equation}
+        %    + 2cos\theta\left[cos^2\theta + \frac{M4(M3+M4)}{M1 M3}\left(\frac{Q}{E1} + 1 - \frac{M1}{M4}\right)\right\]^{\frac{1}{2}}\Bigg\}
+        %    \label{eq:E3}
+        %\end{equation}
+             
+            
+        
+
+
+
     
 
 
@@ -162,9 +204,14 @@ A 2 MeV proton beam is used to annihilate lithium and flourine atoms from a LiF
         \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.}
+            \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 before the cutoff is estimated at 7600 and 18500 and drawn with the blue and purple line, respectively.}
         \end{figure}
 
+        \begin{figure}
+            \center
+            \includegraphics[width=4.5in]{calibration.pdf}
+            \caption{The kinetic energy scale is calibrated to channel number using the Rutherford energies predicted in table~\ref{tab:predictions}. The scale is set where the predicted energy matches 20\% of the maximum before cutoff. The 20\% line is drawn in the same color as its associated maximum line, and same for the identified energy coordinate.}
+        \end{figure}
 
 %─────────────
 \section{Conclusion}

adv_lab.bib

@@ -21,6 +21,23 @@
 
 
 
+@Inbook{Meisel1996,
+author="Meisel, W.",
+editor="Long, Gary J.
+and Grandjean, Fernande",
+title="Surface and Thin Film Analysis by M{\"o}ssbauer Spectroscopy and Related Techniques",
+bookTitle="M{\"o}ssbauer Spectroscopy Applied to Magnetism and Materials Science",
+year="1996",
+publisher="Springer US",
+address="Boston, MA",
+pages="1--30",
+isbn="978-1-4899-1763-8",
+doi="10.1007/978-1-4899-1763-8_1",
+url="http://dx.doi.org/10.1007/978-1-4899-1763-8_1"
+}
+
+
+@book{Ziegler_1975, place={United States}, title={New uses of ion accelerators}, abstractNote={A review is given of new uses of ion accelerators and includes discussion of sample preparation, ion beam and energy selection, detector methods, and data collection and analysis. Topics include: (1) ion-excited x-ray analysis of environmental samples; (2) material analysis by nuclear backscattering; (3) material analysis by means of nuclear reactions; (4) lattice location of impurities in metals and semiconductors; (5) ion implantation in metals; (6) ion implantation in superconductors; (7) ion-induced x-rays from gas collisions; and (8) ion-induced x-rays in solids. A separate abstract was prepared for each chapter for ERDA Energy Research Abstracts (ERA). (PMA)}, publisher={Plenum Press,New York}, author={Ziegler, J.F.}, year={1975}, month={Jan}}
 
 
 @book{tesmer1995handbook,