deletions | additions       diff --git a/Fig_ref_fig_energy_distance_shows__.tex b/Fig_ref_fig_energy_distance_shows__.tex  index 3791198..f32c51f 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 at for  various projectile velocities for the hyper-channeling case. At lower velocities regime, the energy transfer is rather small which support supports  the adiabatic behavior. But at higher velocities aside oscillations of the total energy with the position of the projectile, the total energy of the system increases 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 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 represents 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.