deletions | additions       diff --git a/Recently_from_a_phenomenological_point__.tex b/Recently_from_a_phenomenological_point__.tex  index d87d6db..1623a5a 100644  --- a/Recently_from_a_phenomenological_point__.tex  +++ b/Recently_from_a_phenomenological_point__.tex 
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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} provides both 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.   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 40\% (Fig. \ref{fig:stopping_power}), reveal the stopping due to conduction band electronic excitation 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 a 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}.   In the low energy region the energy loss in metal is due to the excitation of a portion of electrons around the Fermi level to empty states in the conducting band. But at higher energies, a minimum momentum transfer of the projectile is possible due to its short duration close to the target.   In this region the electronic curve has a maximum due to the limited response time of target electrons to the projectile ions.  In this paper we concentrate in the intermediate regime.  In this paper we will address the problem of theoretical calculation of electronic stopping of protons in crystalline $\mathrm{Cu}$ in a wide range of velocities comprising the whole range of available experimental points ($0.01~\mathrm{a.u.} \leq v \leq 10~\mathrm{a.u.}$).   We perform our calculations by directly simulating the process of a proton traversing a crystal of $\mathrm{Cu}$ atoms, producing individual and collective electronic excitations within the TDDFT framework \cite{Correa_2012,Schleife_2012,Schleife_2014}.