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Figure \ref{fig:energy_distance} shows the total electronic energy of the system as a function of position at various projectile velocities for the hyper-channeling case. At lower velocities regime, the energy transfer is rather small which support has as limit  the adiabatic behavior. But at higher velocities aside 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 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 corresponding lattice positions of the projectile.