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%\section{Conclusion}  Finally, we point out that the investigation of the low velocity limit of stopping is important for the understanding of  the non-adiabatic coupling between ions and electrons \cite{Caro_2015} and also for modeling dissipative molecular dynamics \cite{Caro_1989}\cite{Duffy_2006}. In simulations of radiation events the final state is precisely controlled by dissipation in the late stages when ions move slowly but still non-adibatically.  In summary, in this paper Letter  we have reported the $S_\text{e}$ of protons in copper in a very wide range of velocities. TDDFT-based electron dynamics is able to capture 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 find a collapse of the two curves at low velocities velocities;  and identified five regimes i) the linear $s$-only ($0.02-0.1~\mathrm{a.u.}$), ii) linear $s+d$ ($0.3-1~\mathrm{a.u.}$), iii) crossover with $1.5$-power law ($0.1-0.3~\mathrm{a.u.}$), iv) plasmon-like ($v > 1~\mathrm{a.u.}$) and v) what is possibly a non-linear screening regime at $v < 0.02~\mathrm{a.u.}$.   This is a further illustration that the electronic stopping in general does not have a simple behavior in the limit $v\to 0$, and that band and bound effects dominate this behavior.