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accelerator lab

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accelerator/report/report.tex
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@ -77,13 +77,6 @@ A 2 MeV proton beam is used to annihilate lithium and flourine atoms from a LiF
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.
%\subsection{Rutherford Scattering}
\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 $\theta = 149.95\degree\pm0.05\degree$. We define a kinetic factor K such that the kinetic energy of the scattered proton $E3 = K\times E1$. If the collision is elastic, this kinetic factor
\begin{table}
\center
\begin{tabular}{rl}
@ -96,6 +89,36 @@ A 2 MeV proton beam is used to annihilate lithium and flourine atoms from a LiF
\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{tabular}{rl}
Species & Mass \\
\hline
$^7$Li & \\
$^19$F & \\
Cu & \\
Si & \\
p & \\
$\alpha$ & \\
\end{tabular}
\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{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}
\begin{equation}
K = \left(\frac{M1 cos(\theta) + \left(M2^2 - M1^2sin^2(\theta)\right)^{1/2}}{M1 + M2}\right)^2.
\end{equation}
\begin{figure}