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Edwin E. Quashie edited At_low_velocity_our_results__.tex
almost 8 years ago
Commit id: b03e43bf615c1b4076ca0e01c1eaa9e51280e42f
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This could be a simple experimental scaling issue related to the difference between measuring relative and absolute stopping power at low velocities \cite{Markin_2009}.
We expect similar results for other transition metals, as described by Ref.~\cite{Markin_2008}.
Below
$0.02~\mathrm{a.u.}$, $0.07~\mathrm{a.u.}$, the lack of experimental points precludes a direct comparison, but we find
a large deviation from linear
behavior. 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 integration.
One possible explanation is that bound effects break down the linear response (Lindhard) approximation that was useful to interpret the different regimes (and crossover) for velocities above $0.02~\mathrm{a.u.}$.
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 possibly related to bound effects.
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_2015} where analogous band and gap threshold effects have been found.
%
%Below $0.02~\mathrm{a.u.}$, the lack of experimental points precludes a direct comparison, but we find a large deviation from linear behavior.
%One possible explanation is that bound effects break down the linear response (Lindhard) approximation that was useful to interpret the different regimes (and crossover) for velocities above $0.02~\mathrm{a.u.}$.
%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 possibly related to bound effects.
%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_2015} where analogous band and gap threshold effects have been found.%