deletions | additions       diff --git a/Recently_from_a_phenomenological_point__.tex b/Recently_from_a_phenomenological_point__.tex  index 7fbd382..a8b0fbd 100644  --- a/Recently_from_a_phenomenological_point__.tex  +++ b/Recently_from_a_phenomenological_point__.tex 
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%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 this paper Letter  wewill  address the problem of theoretical calculation calculation, under a single theory,  of $S_\text{e}$ of protons in crystalline $\mathrm{Cu}$ in a wide range of velocities comprising the whole and beyond the 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}.  We provide an interpretation of the results and comparison with experiments.