deletions | additions       diff --git a/Figure_ref_fig_stopping_power_shows__.tex b/Figure_ref_fig_stopping_power_shows__.tex  index 79bd07b..eb9811b 100644  --- a/Figure_ref_fig_stopping_power_shows__.tex  +++ b/Figure_ref_fig_stopping_power_shows__.tex 
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Similar effects were also reported earlier by Mao \emph{et al} for SiC by $\mathrm{H^+}$ and $\mathrm{He^{2+}}$ \cite{Mao_2015}, when the ion velocity exceeds certain value, a mechanism   known as the plasma oscillations \cite{Bauer_1990} of the target electrons, for the electronic energy loss appears; present TDDFT describe it pretty well.   For the off-channeling case, there is a better agreement between the our $S_\text{e}$ results with the \textsc{Srim} data in most of the range. Presumably in In  experiments where trajectories are not finely  controlled, the projectile does indeed explore core regions of the host atoms. At higher velocities ($v > 4 ~\mathrm{a.u.}$) the disagreement stems from combined effect of the lack of explicit core electrons in the simulation and also size effects, as excitations of long wavelength plasma oscillation is constrained by the simulation supercell \cite{Schleife_2015}.   It is clear that a larger cell and the inclusion of more core electrons would be necessary to obtain better agreement in this region.   Giving the limitation of the orbital based method it is reasuring reassuring  to see agreement up to a few times the velocity of the maximum stopping. We also see that at low velocity the off-channeling and channeling simulated points collapses to a common curve, this effect has been seen in the simulations before \cite{Schleife_2015,Ullah_2015}, at low velocity the effect is less sensitive to the precise geometry of the trajectory. 
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For energy loss our new results for $v \leq 0.06~\mathrm{a.u.}$, are primarily due to $s$-band electrons.   In the simulation we directly show a crossover region between the two linear regimes, and we find that the friction in direct proportion to the velocity with a power law of with exponent $1.455$.  The kink found at $v = 0.6~\mathrm{a.u.}$ can be explained by conservation laws of in  the homogeneous electron gas. The minimum e energy loss with maximum momentum transfer from an electron to an ion moving with velocity $v$ are respectively $2\hbar k_\text{F}$ and $2\hbar k_\text{F} v$ (plus corrections of order $m_\text{e}/m_\text{p}$). Therefore electrons in the range $E_\text{F} \pm 2\hbar k_\text{F} v$ can participate in the stopping process.   Taking into account that DFT band structure predicts that the $\mathrm{d}$-band is $\sim 1.5~\mathrm{eV}$ below the Fermi energy, and we use that the values of the effective mass are close to $1$ for and $k_\text{F}$ $\mathrm{s}$-electrons  Below $0.02~\mathrm{a.u.}$, the lack of experimental points preclude a direct comparison, but we find a large deviation from linear behavior, one possible explanation is that bound effects break down the linear response (Linhard) approximation that was useful to interpret the different regimes and crossover at $v > 0.02~\mathrm{a.u.}$