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William edited section_Theory_me_as_well__.tex
over 8 years ago
Commit id: 1603c75114e6ed7a0eb0dff0ca15e06b498da9c6
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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 $1.634
\frac{kg}{m^{3}}, \frac{kg}{m^{3}}$, 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.
After reaching the lowest excitation energy $E_{a}$, the electrons move an additional distance, $\lambda$. Over this distance the electrons gains an additional energy $\Delta E_n \deta_n$.
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]}