deletions | additions       diff --git a/Figure_ref_fig_force_on_neighbor_shows__.tex b/Figure_ref_fig_force_on_neighbor_shows__.tex  index b4a8b55..1d237c4 100644  --- a/Figure_ref_fig_force_on_neighbor_shows__.tex  +++ b/Figure_ref_fig_force_on_neighbor_shows__.tex 
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Figure Fig.  \ref{fig:force_on_neighbor} shows the radial force exerted on a neighboring 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 forces on the nuclei are evaluated using the time-dependent electron density, $n(\mathbf{r}, t)$. 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 maximum value for the force is obtained at the closest distance between $\mathrm{H^+}$ and neighbor $\mathrm{Cu}$ atom.