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Alfredo A. Correa edited Recently_from_a_phenomenological_point__.tex
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Recently, from a phenomenological point of view, Uddin \emph{et al.} \cite{Alfaz_Uddin_2013} have calculated $S_\text{e}$ for protons, $\alpha$ and $\mathrm{He}$ for various media with atomic number $Z=2$ to $100$ using realistic electron density with four fitted parameters and obtained $\sim 12\%$ agreement with the \textsc{Srim} data \cite{Ziegler_2010}.
Using a single formula with fewer parameters Haque \emph{et al.} \cite{Haque_2015} have reported proton stopping power with encouraging results. For example, at their lowest reported velocity $v = 0.6 ~\mathrm{a.u.}$, their results are within $\sim 15\%$ of our \emph{ab initio} findings for $\mathrm{H}$ in $\mathrm{Cu}$.
\textsc{Srim} \cite{Ziegler_2010}
also provides both a fitted model for electronic stopping as well as a large set of experimental points, at low velocities both experiment and the fitted models becomes more scarce and less reliable.
The recent measurements by Cantero \emph{et al.} \cite{Cantero_2009} and by Markin \emph{et al.} \cite{Markin_2009} of slow ($v \leq 0.6~\mathrm{a.u.}$) $\mathrm{H^+}$ in $\mathrm{Cu}$, although disagreeing with each other in absolute scale by $\sim 40\%$ (Fig. \ref{fig:stopping_power}), both reveal the stopping due to conduction band electronic excitations at lower velocity, evidenced as a change in slope.
The combined effects of both the free electrons and the loosely bound $\mathrm{d}$-electrons causes the change of the slope \cite{Goebl_2013}.