deletions | additions       diff --git a/Fig_ref_fig_energy_distance_shows__.tex b/Fig_ref_fig_energy_distance_shows__.tex  index 73b680c..39f7272 100644  --- a/Fig_ref_fig_energy_distance_shows__.tex  +++ b/Fig_ref_fig_energy_distance_shows__.tex 
...
\section{Results}  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 smaller, approaching the adiabatic behavior, while at higher velocities (aside oscillations of the total energy with the position of the 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 to a steady rate.