deletions | additions       diff --git a/Recently_from_a_phenomenological_point__.tex b/Recently_from_a_phenomenological_point__.tex  index bdfefd7..c219b58 100644  --- a/Recently_from_a_phenomenological_point__.tex  +++ b/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 experimental data becomes more scarce and the fitted models less reliable.   Fitted models tend to extrapolate linearly from the lowest point to zero velocity, possibly leaving out important physics that we try to investigate here.  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. slope near $v=0.1 or 0.15~\mathrm{a.u.}$.  The combined effects of both the free electrons and the loosely bound $\mathrm{d}$-electrons causes the change of the slope \cite{Goebl_2013}.  %This study supports this even down to $v = 0.02 ~\mathrm{a.u.}$ (see Figure \ref{fig:log_stopping_power}).   %The experimental results of Nomura and Kiyota \cite{Nomura_1975} on $\mathrm{H^+ + Cu}$ film show the dependence of $S_\text{e}$ on incident velocity agrees with the calculation of Lindhard \emph{et al.} \cite{Lindhard_Scharff_Schiott}.