deletions | additions       diff --git a/Recently_from_a_phenomenological_point__.tex b/Recently_from_a_phenomenological_point__.tex  index 12f157c..895595b 100644  --- a/Recently_from_a_phenomenological_point__.tex  +++ b/Recently_from_a_phenomenological_point__.tex 
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%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 Letter we will address the problem of theoretical calculation 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 \cite{Correa_2012,Schleife_2012,Schleife_2014} including Ehrenfest molecular dynamics (EMD) \cite{Gross_1996,Calvayrac_2000,Mason_2007,Alonso_2008,Andrade_2009}. This method is used to calculate most microscopic quantities along the process (forces, electronic density, charges, etc); in particular, we report here calculation of $S_\text{e}$. A quantitative explanation and interpretation of our results are furnished along with a detailed experimental comparison.  %We  provide a quantitative explanation and interpretation of the result and a comparison with experiments. %In recent years, the development of time-dependent methods have enhanced the diverse study of many body problems involving the slowing down of charged projectiles both in solids and gases. The time dependent density functional theory (TDDFT) on the other hand has enjoyed much consideration owing to its electron dynamics both self-consistency and non-perturbative way.  %