deletions | additions       diff --git a/Fig_ref_fig_energy_distance_shows__.tex b/Fig_ref_fig_energy_distance_shows__.tex  index f32c51f..73b680c 100644  --- a/Fig_ref_fig_energy_distance_shows__.tex  +++ b/Fig_ref_fig_energy_distance_shows__.tex 
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Fig. \ref{fig:energy_distance} shows the total electronic energy of the $\mathrm{H^+ + Cu}$ system as a function of position for various projectile velocities for the hyper-channeling case. At a  lower velocities regime, the energy transfer is rather small which supports smaller, approaching  the adiabatic behavior.   But behavior, while  at higher velocities aside (aside  oscillations of the total energy with the position of the projectile, projectile)  the total energy of the system increases linearly  with time. After the projectile travels some short distance in the crystals ($\sim 5~a_0$) the increase in total energy of the system stabilizes at to  a steady rate. At that stationary state, the $S_\text{e}$ is then extracted from the average slope of the total energy vs. projectile displacement; these represent the energy gained by the target or the energy loss of the projectile.  Hence a stationary regime is reached and the difference in energy ($\Delta E$) remains constant for the corresponding lattice positions of the projectile.