deletions | additions       diff --git a/In_order_to_interpret_the__.tex b/In_order_to_interpret_the__.tex  index e67eba5..bf7b605 100644  --- a/In_order_to_interpret_the__.tex  +++ b/In_order_to_interpret_the__.tex 
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In order to interpret the results we calculated the linear response stopping $S_\text{L}(n, v)$ \cite{Lindhard_1964} based on the Linhard RPA dielectric function $\epsilon_\text{RPA}$ for different effective densities $n$ \cite{Giuliani_2005}.  \begin{equation}  S_\text{L}(n, v) = \frac{2 e^2}{\pi v^2} \int_0^\infty \mathrm{d}k k^{-1} \frac{\mathrm{d}k}{k}  \int_0^{k v} \mathrm{d}\omega\omega \Im 1/\varepsilon_\text{RPA}(n, \frac{1}{\varepsilon_\text{RPA}(n,  k, \omega) \omega)}  \end{equation}  (which assumes a proton effective charge of $Z_1 = 1$).  As shown in Fig.~\ref{fig:log_stopping_power}, for $v < 0.1~\mathrm{a.u.}$ the results mimics the response of an electron gas with one electron per $\mathrm{Cu}$ atom.