deletions | additions       diff --git a/thFig_ref_fig_stopping_power_shows__.tex b/thFig_ref_fig_stopping_power_shows__.tex  index 23af4a0..e95c9f0 100644  --- a/thFig_ref_fig_stopping_power_shows__.tex  +++ b/thFig_ref_fig_stopping_power_shows__.tex 
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Fig. \ref{fig:stopping_power} shows a comparison of our calculated $S_\text{e}$ with \textsc{Srim}-based model and experimental data.   In the \emph{channeling} case, the maximum of our calculated  stopping is lower in value and velocity compared to the \textsc{Srim} database and the \emph{off-channeling}, after the maximum \emph{off-channeling} case, and  it decreases faster. faster after the maximum.  For the off-channeling case, there is a better agreement between our $S_\text{e}$ results with the \textsc{Srim} data in most of the range.   In experiments, where trajectories are not necessarily finely controlled, the projectile does indeed explore core regions of the host atoms, and that is presumably why off-channeling simulations are a better representation for the most common experiments \cite{Dorado_1993}.   At higher velocities ($v > 4 ~\mathrm{a.u.}$) further disagreement stems from combined effect of the lack of explicit deeper core electrons in the simulation and also size effects, as excitations of long wavelength plasma oscillations are artificially constrained by the simulation supercell \cite{Schleife_2015}.  It is clear that a larger cell and eventually the inclusion of more core electrons would be necessary to obtain better agreement in this region. high velocity region that is out the of scope of this article.  %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 have a dramatic effects 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.   Although experimental values have considerable vertical spread,   our calculated stopping power is on the low side for most of the points and also below the fitted by \textsc{Srim} model \cite{Ziegler_2010}.  While this was partially explained by taking into account off-channeling trajectories near the maximum of stopping,   there are other  possible intrinsic limitations of the approximations to the density functional theory used. Along this line line,  we would like to note that more sophisticated approaches, based on the dielectric and current-density response but including  the exact many-body and dynamic exchange-correlation  treatment, are available in the literature \cite{Nazarov_2007}.   This type of advanced approaches which are beyond the current scopeof this work  contain explicitly additional channels of dissipation not taken into account   in our adiabatic exchange and correlation functionals, which can be relatively important.  Given the aforementioned limitations of the orbital based method and the exchange and correlation used it   is still reassuring to see agreement up to a few times the velocity of the maximum stopping. stopping and gives us confidence to make predictions in the lower velocity regime.  At low velocity it is observed that the off-channeling and channeling simulated results collapse into a common curve,   this effect has been seen in the simulations before \cite{Correa_2012,Schleife_2015,Ullah_2015}.