deletions | additions       diff --git a/Recently_from_a_phenomenological_point__.tex b/Recently_from_a_phenomenological_point__.tex  index c308a3d..cda32ec 100644  --- a/Recently_from_a_phenomenological_point__.tex  +++ b/Recently_from_a_phenomenological_point__.tex 
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It has enjoyed much consideration owing to its electron dynamics both self-consistency and non-perturbative way \cite{Kohn_1965} and allowed from an atomistic \emph{ab initio} perspective.  In studying the role of ion-solid interactions in $\mathrm{H^+ + Al}$, Correa {\emph et al} \cite{Correa_2012} have shown that the electronic excitations due to molecular dynamics (MD) are quite different from the adiabatic outcome. Even today the inclusion of non adiabatic effects in a real calculation poses a challenging problem. Recently Schleife {\emph et al} \cite{Schleife_2015} have calculated the electronic stopping $\mathrm(S_\text{e})$ by $\mathrm{H}$ and $\mathrm{He}$ projectile including non-adiabatic interactions and found that off-channeling trajectories along with the inclusion of semicore electrons enhance $\mathrm{S_\text{e}}$ resulting better agreement with the experiment.   The recent measurement \cite{Cantero_2009} by slow $\mathrm{H^+}$ in $\mathrm{Cu}$ reveals the stopping due to conduction band electronic excitation at lower velocity. The combined effects of both the free electrons and the loosely bound $d$ electrons causes a change of the slope. This study supports this even upto $v = 0.01 ~\mathrm{a.u.}$ (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 $\mathrm{S_\text{e}}$ 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.   We report here an application of the TDDFT that embodies a plane-wave basis set that represents accurately the electron dynamics \cite{Correa_2012,Schleife_2012,Schleife_2014} for proton impact collision of $\mathrm{Cu}$ crystal. The suitability of this method is tested by evaluating the $\mathrm{S_\text{e}}$.  Our results are compared with those of \textsc{Srim} as well as available experimental values.%  %  %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.  %  %Using a quantal method based on TDDFT, Quijada {\emph et. al.} \cite{Quijada_2007} have studied the energy loss of protons and anti-protons moving inside metalic Al and obtained good results for the projectile-target energy transfer over a wider energy range.