phy-4660/accelerator/report/report.tex

\documentclass[11pt,letterpaper]{article}

%\usepackage{aas_macros}
\usepackage{biblatex}
\usepackage{graphicx}
\usepackage[margin=1.in,centering]{geometry}
\usepackage{hyperref}
\usepackage{caption}
\usepackage[export]{adjustbox}
\usepackage{float}
\usepackage{gensymb}

\bibliography{/home/caes/wmu/phy-4660/adv_lab.bib}

\begin{document}


\newcommand{\FpaO}{$^{19}\textrm{F(p,}\alpha)^{16}\textrm{O}$}
\newcommand{\LipaHe}{$^7\textrm{Li(p,}\alpha)^4\textrm{He}$}

%\newcommand{}$^7\textrm{Li(p,}\alpha)^4\textrm{He}$ reaction.\\






\title{Lab 4: Nuclear Reactions and Nucleosynthesis}
\author{Otho Ulrich, Eugene Kopf, Asghar Kayani, Mike Pirkola, }
\maketitle

\begin{abstract}
\end{abstract}

%─────────────
\section{Introduction: Lithium and Fluorine}
    \label{sec:intro}
    The nuclear properties of lithium are of interest, especially its interaction probability cross-section. Studies of the Sun's photosphere show the abundance of lithium relative to hydrogen and helium to be nearly an order-of-magnitude less. Lithium's large cross-section is believed responsible; it predicts that ionized hydrogen will readily collide with lithium, transforming the lithium to helium, and emitting an alpha particle. This is one transition that takes place in stellar nucleosynthesis, as lithium is carried toward a star's core by convective currents, but even with this process and reaction in mind, modern astrophysicists have yet to completely explain the lack of abundant lithium in our sun's photosphere, named the Solar Lithium Problem. Studies of the nuclear properties of lithium could elucidate a better stellar structure model, but this is outside the scope of our study. \cite{Carroll&Ostlie}

    Fluorine can be annihilated in a similar fashion. It is one of the rarest elements observed by astronomers, and thought to be for the same reasons: it is readily annihilated by a proton to produce oxygen and an alpha particle. Figure \ref{fig:abundances} shows relative abundances of many elements. To judge whether this explanation is plausible, we will determine the probability cross-sections of the fluorine-proton reaction {\FpaO} and the lithium-proton reaction {\LipaHe}. By observing the alpha particle products of each reaction, these cross-sections can be computed.\\

    \begin{figure}
        \center
        \includegraphics[width=4.5in]{../abundances.png}
        \caption{Relative elemental abundances in the sun's photosphere. Lithium and fluorine are much less abundant than their neighbour elements. It is thought this is due to large probability cross-sections for a proton collision with these nuclei. \cite{Carroll&Ostlie}}
        \label{fig:abundances}
    \end{figure}

\section{Detector}
    \label{sec:detector}
    

\section{Nuclear Reactions and Detection Plan}
    \label{sec:beamreactions}
    
    The nuclear reactions and \FpaO and \LipaHe are of interest, and both can be analyzed using the kinematic diagram in figure \ref{fig:kinematics}. In the case where the incident particle M1 does not have sufficient kinetic energy to overcome the electric potential barrier of the target nucleus, Rutherford scattering will occur, and the incident particle will backscatter without annihilating the target nucleus. 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.

    \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 $\theta = 149\pm0.05\degree$ \cite{ADVLABACCEL}.}
        \label{fbig:kinematics}
    \end{figure}


%─────────────    
\section{Reverberation Mapping}
    \label{sec:reverbmap}


%─────────────
\section{Analysis of Reverberating Lightcurves}
    \label{sec:analysis}

    \subsection{Time Delay and Transfer Function Theory}
        \label{subsec:transferfunc}



    \subsection{Computational Details}
        \label{subsec:computation}


%─────────────
\section{Results}
\label{sec:results}

\section{Conclusion}
    \label{sec:conclusion}

\printbibliography


\end{document}