William edited section_Theory_me_as_well__.tex  over 8 years ago

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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]}