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Edwin Quashie edited section_Computational_and_Theoretical_Details__.tex
almost 9 years ago
Commit id: bcfaaa9a6da73bb6145ea8fbf29c9e7b2b861630
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The time-dependent KS equation was then solved numerically by explicit time-integration scheme as described in \cite{Schleife_2012}. A time step of $0.121 attoseconds$ was used which is below the stability limit for the numerical explicit time-integration scheme for these type of basis set. The wave functions were then propagated for several $femtoseconds$.
The total electronic energy $\mathrm(E)$ of the electronic system changes as a function of the projectile position $\mathrm(x)$ since the projectile deposits energy into the electronic system as it moves through the host atoms. The increase of
$\mathrm(E)$ $\mathrm{E}$ as a function of projectile displacement
$\mathrm(x)$ $\mathrm{x}$ enables us to extract the electronic stopping power
\begin{equation}
S(x) S_e(x) = \frac{dE(x)}{dx}
\label{eq:stopping}
\end{equation}
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