At low velocity, our results show good agreement with the experiments of Markin et al. \cite{Markin_2009} but in relative disagreement with the measurements of Cantero et al. \cite{Cantero_2009} and the Srim model. The difference between experiments could be due to a simple experimental scaling issue related to the difference between measuring relative and absolute stopping power at low velocities \cite{Markin_2009}.

Below \(0.07~\mathrm{a.u.}\), the lack of experimental points precludes a direct comparison, but we find linear behavior at least down to \(0.02~\mathrm{a.u.}\). Below \(0.02~\mathrm{a.u.}\) the direct real time integration becomes less efficient and the accuracy is compromised by the quality of the numerical time integrator and the number of steps necessary to complete a calculation \cite{Schleife_2012}. Probing this regime experimentally would be rather difficult, especially to disentangle it from nuclear stopping effects, but if this is confirmed it would be an unexpected new regime. In any case, the combination of experimental and theoretical results shows that the limit \(v\to 0\) is intricate for metals as it is for insulators \cite{Artacho_2007, Lim_2016} where analogous band and gap threshold effects have been found.

Finally, we point out that the investigation of the low velocity limit of stopping power 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,Duffy_2006} where electrons act both as a thermal bath and a friction media. 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 \cite{Zarkadoula_2014}.