deletions | additions       diff --git a/We_observe_in_Fig_ref__.tex b/We_observe_in_Fig_ref__.tex  index 311d1c7..0a8fc27 100644  --- a/We_observe_in_Fig_ref__.tex  +++ b/We_observe_in_Fig_ref__.tex 
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We observe A log--log plot of the findings of Fig. \ref{fig:stopping_power} is depicted  in Fig.~\ref{fig:log_stopping_power} Fig.~\ref{fig:log_stopping_power}, where we have observed  that the resulting curve is not as particularly simple. In order to interpret the results we also calculated the linear response stopping $S_\text{L}(n, v)$ \cite{Lindhard_1964_book} based on a simple Lindhard RPA dielectric function $\varepsilon_\text{RPA}$ for different effective densities $n$ of the homogeneous electron gas~\cite{Giuliani_2005}  \begin{equation}  S_\text{L}(n, v) = \frac{2 e^2}{\pi v^2} \int_0^\infty \frac{\mathrm{d}k}{k} \int_0^{k v} \omega\mathrm{d}\omega \Im\left(\frac{1}{\varepsilon_\text{RPA}(n, k, \omega)}\right)