deletions | additions       diff --git a/Fig_ref_fig_force_on_neighbor_shows__.tex b/Fig_ref_fig_force_on_neighbor_shows__.tex  index 51e003e..e7bb294 100644  --- a/Fig_ref_fig_force_on_neighbor_shows__.tex  +++ b/Fig_ref_fig_force_on_neighbor_shows__.tex 
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%Fig. Fig.  \ref{fig:force_on_neighbor} shows the radial force exerted on a neighboring $\mathrm{Cu}$ atom closest to $\mathrm{H^+}$ trajectory as a function of parallel distance to the projectile at different projectile velocities.% along the [100] channeling trajectory. %The The  forces on the nuclei are evaluated using the time-dependent electron density, $n(\mathbf{r}, t)$. %The The  force is obtained by the application of the Hellmann-Feynman theorem \cite{Hellmann_2015,1941,Feynman_1939}. The adiabatic force is recovered for $v \to 0$ with no oscillations as expected.   %The The  maximum value for the force is obtained at the closest distance between $\mathrm{H^+}$ and neighbor $\mathrm{Cu}$ atom. %As As  the proton moves away from the $\mathrm{Cu}$ atom, the force decreases significantly and eventually reduces to zero. %As As  the velocity increases the position of the maximum value of the force shifts due to the complex shape-structure of the curves and results oscillations. These oscillations in the force persist for velocities above $1.0 ~\mathrm{a.u.}$, an interpretation in terms of plasmon excitations is given in \cite{Correa_2012}. %These oscillations becomes persistent as the velocity of the proton increases.%