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William edited section_Theory_me_as_well__.tex
over 8 years ago
Commit id: 207843d9f543371a2648e238b2a230fa744854c0
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\begin{equation}\label{eq:ShortMeanFreePath}
\Delta E_{\textrm{atom}} = \Delta E_{\textrm{electron}} \textrm{ [eV]}
\end{equation}
For a high density gas,
where atoms are very close together, it is likely that electrons will move a very short distance before colliding inelastically with an atom, and equation 2 becomes an excellent approximation. At STP, the densities of Neon vapor and Argon vapor are $0.8244 \frac{kg}{m^{3}}$ and $1.634 \frac{kg}{m^{3}}, and so they are relatively low density gases. In \cite{Rapior_2006} it was discovered that for low density gases, the distance that electrons travel before an inelastic collision is large enough that it is indeed significant.
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]}