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Figure \ref{fig:energy_distance} shows the total electronic energy of the system as a function of position for different projectile velocities for the hyper-channeling case. At lower velocities regime, there is negligible/no net energy transfer. The adiabatic behavior is recovered. 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 covers some short distance in the crystals (\sim 5a_0) the increase in total energy of the system stabilizes at a steady rate. Hence a stationary regime is reached and the difference in energy remains constant for corresponding lattice positions of the projectile. The S_e $S_e$  is then extracted from the average slope of the total energy vs. projectile displacement at the stationary state. These represents the energy gained by the target or the energy loss of the projectile.