deletions | additions       diff --git a/Recently_from_a_phenomenological_point__.tex b/Recently_from_a_phenomenological_point__.tex  index 4977c46..c308a3d 100644  --- a/Recently_from_a_phenomenological_point__.tex  +++ b/Recently_from_a_phenomenological_point__.tex 
...
The development of time dependent density functional theory (TDDFT) \cite{Runge_1984} enhanced the diverse study of many body problems and in particular the problem at hand.   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 radiation damage ion-solid interactions  in $\mathrm{H^+ + Al}$ interactions 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.