deletions | additions       diff --git a/Fig_ref_fig_force_on_neighbor_shows__.tex b/Fig_ref_fig_force_on_neighbor_shows__.tex  index 93a7e42..f46d37c 100644  --- a/Fig_ref_fig_force_on_neighbor_shows__.tex  +++ b/Fig_ref_fig_force_on_neighbor_shows__.tex 
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The maximum value for the force is obtained at the closest distance between the $\mathrm{H^+}$ and a neighbor $\mathrm{Cu}$ atom.  As the proton moves further from the $\mathrm{Cu}$ atom, the force decreases and eventually reduces to zero.   As the velocity increases the position of the maximum value of the force first shifts and later results in persistent oscillations.  The existence of plasma oscillations is detected in our simulations by persistent charge motion above a certain threshold velocity of $v \simeq 1.0~\mathrm{a.u.}$.   This plasma oscillations this effect in the components forces over individual $\mathrm{Cu}$ atoms near the track of the passing hydrogen (Fig.~\ref{fig:force_on_neighbor}). This forces persist (and oscillate) even after the proton has passed.  %These oscillations remain persistent with the increase of projectile velocity.% of the proton increases.%