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\title{Lab 1: Alpha Spectroscopy}
\author{Otho Ulrich}

\date{January 26, 2017}

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\begin{abstract}

Alpha-particle spectra of Americium$^{42}$ are collected across an open path through an evacuated chamber and across 25, 50, and 100 microinch absorption depths of nickel foil. A totally depleted silicon surface barrier detector model !!!MODELNUMBER provides a voltage response proportional to the kinetic energy of the particle it absorbs, and this response is used to produce an energy-count spectrum for each setup. The mean kinetic energy of the particles incident on the detector for each case are compiled to create a curve describing the attenuation as a function of absorption depth. The alpha-particle spectrum of a radium sample is also analyzed, and four alpha-particle peaks associated with the decay chain beginning with radium are identified.

\end{abstract}


\section{Introduction}
\label{sec:intro}

Spectroscopy of alpha radiation is a method for testing and measuring the properties of any alpha emitter, which is a class of radioactive particles that emit alpha particles, a bound collection of two protons and two neutrons. This is one of the primary classes of radiation, along with beta and gamma radiation, and of these the only hadronic form of radiation. An alpha particle is emitted during alpha decay of a nucleus, when the nucleus gives off 2 protons and 2 neutrons. The isotope loses 2 from its atomic number, decaying into an isotope of a new element. The spectrum measured from the radium sample exemplifies this, as the radium decays into daughter elements further down the periodic table. Alpha particles created in this process often have kinetic energy near 5 MeV and are highly ionizing, but with a small penetration depth. They are therefore not considered a dangerous form of radiation unless ingested.


\section{Alpha Detector and Energy Scale}
\label{sec:reverbmap}
A totally depleted silicon surface barrier (ORTEC model B) is used to count alpha particles emitted by samples used in this study. This detector absorbs alpha particles, transducing their kinetic energy into electronic activity. The potential difference output from the detector is proportional to the kinetic energy of the absorbed alpha particle, and these variable voltage signals were collected to generate each energy spectrum. 

    \subsection{Continuum Reverberation}
    \label{sec:cont_reverb}
    
\section{Analysis}
\label{sec:analysis}
The energy scale is calibrated by setting the mean of the peak of unimpeded alpha particles emitted by the Americium source to the experimentally-determined value 

 $\frac{\Delta E}{\Delta X}$



    \begin{equation}
        \label{eq:timelag}
        \tau\left(\lambda\right) = 
            \left(3.9 \textrm{d}\right) 
            \left(\frac{T_0}{10^4\mathrm{K}}\right)^{4/3}
            \left(\frac{\lambda}{10^4\mathrm{\AA}}\right)^{4/3}
            \left(\frac{X}{4}\right)^{4/3}
    \end{equation}

    \begin{figure}
        \centering
        %\includegraphics[width=2.5in]{../img/basic_geometry.png}
        \caption{Simple geometry of reverberation in the accretion disk. Some continuum emission is reprocessed before escaping toward the observer.}
        \label{fig:disk_reverb}
    \end{figure}


    \begin{figure}
        \centering
        \begin{minipage}{.475\textwidth}
            \centering
            %\includegraphics[width=1\linewidth]{../img/tophat_timedomain.pdf}
            \captionof{figure}{Tophat transfer functions in the time domain show an average time lag of the reverberating curve and a constant distribution in time over an interval. An area of unity indicates no loss of signal in the response.}
            \label{fig:th_time}
        \end{minipage}
        \hfill
        \begin{minipage}{.475\textwidth}
            \centering
            %\includegraphics[width=1\linewidth]{../img/tophat_freqdomain.pdf}
            \captionof{figure}{The time lags associated with each tophat function. Distinct features related to the average time lag are present (maximum, value of $\nu$ at steepest change), and complicated relationships with higher frequency waves can be noted.}
            \label{fig:th_freq}
        \end{minipage}
    \end{figure}



\section{Discussion}


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%  Leslie Lamport,
%  \emph{\LaTeX: a document preparation system},
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%  1994.
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