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\section{Conclusion}  Insummary, in  this paper we have reported the $S_\text{e}$ of protons in copper in a very wide range of velocities. TDDFT-based electron dynamics is capable of capturing most of the physics in the different ranges, starting from non-linear screening effects, electron-hole excitations and production of plasmons.   We disentangled channeling and off-channeling effects and observe a collapse of the two curves at low velocities; and identified five regimes  i) the linear $\mathrm{s}$-only ($0.02-0.07~\mathrm{a.u.}$),