this is for holding javascript data
Alfredo A. Correa edited In_order_to_interpret_the__.tex
over 8 years ago
Commit id: fba3fc6ac5649bda6f2aa8c36f0d10232cf30b15
deletions | additions
diff --git a/In_order_to_interpret_the__.tex b/In_order_to_interpret_the__.tex
index a5a658e..deac3d6 100644
--- a/In_order_to_interpret_the__.tex
+++ b/In_order_to_interpret_the__.tex
...
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} \int_0^{k v} \mathrm{d}\omega\omega
\Im {1/\varepsilon_\text{RPA(n, \Imag 1/\varepsilon_\text{RPA(n, k, \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.