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\section{Insert Theory Section HERE}  Contrast two predictions:  \begin{enumerate}  \item  in the short mean free path limit, $\Delta \begin{equation}\label{eq:ShortMeanFreePath}   \Delta  E_{\textrm{atom}} = \Delta E_{\textrm{electron}} \textrm{ [eV]}$  \item [eV]}  \end{equation}  in long mean free path limit, $ \begin{equation}\label{eq:LongMeanFreePath}  \Delta E__{\textrm{atom, n}} = E_n - E_{n-1} = [1+ \frac{\lambda}{L} {(2n-1)}] E_a \textrm{ [eV]}$  \end{enumerate} [eV]}  \end{equation}  where $E_n = e V_{\textrm{acceleration}} $ is the energy of the electron at the \textit{nth} dip in electron beam current (indicating transfer of energy from electron to atom), and the mean free path $\lambda$ depends on the gas density, pressure, and temperature.   Explain how and when they differ, when they agree, and how you would determine from your data which would be the appropriate choice for analysis?