deletions | additions       diff --git a/section_Theory_cite_Melissinos_as__.tex b/section_Theory_cite_Melissinos_as__.tex  index 40b134f..759a367 100644  --- a/section_Theory_cite_Melissinos_as__.tex  +++ b/section_Theory_cite_Melissinos_as__.tex 
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\Delta E__{\textrm{atom, n}} = E_n - E_{n-1} = [1+ \frac{\lambda}{L} {(2n-1)}] E_a \textrm{ [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. When $\lambda$ is very small (as is the case for a high density) gas, the second term ($\frac{\lambda}{L} {(2n-1)}E_a$) will cancel, and the expression for the long mean free path will be equivalent to the expression for the short mean free path. Since the three gases used were low-density gases, the second term is significant, and the expression for the long mean free path must be used.  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?