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\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. After reaching the lowest excitation energy $E_{a}$, the electrons move an additional distance, $\lambda$. Over this distance the electrons gains an additional energy $\Delta E_n \delta_n$. Thus for $n$ inelastic collisions, the energy gained is:   \begin{equation}\label{eq:EnergyGained}   \E_n \ E_{n}  = n(E_a+\delta_n) \end{equation}  Assuming that the experiment took place at typical tube pressures $\lambda$ should be much smaller than the distance between $G_{1}$ and $G_{2}$. Thus $\delta_{n}\ll E_{a}$ and:   \begin{equation}\label{eq:EnergyGained}   \\delta_{n} \ \delta_{n}  = n\frac{\lambda}{L}E_{a} \end{equation}  Combining Equations 2 and 3, an expression for the long mean free path limit can be written:   \begin{equation}\label{eq:LongMeanFreePath}