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\section{Introduction}  Thecharged particle  interaction of charged particles  with matter has been a subject of extensive research over many decades; it findings provide precise information for many technological applications such as nuclear safety, applied material science, medical physics and fusion and fission applications \cite{Komarov_2013,Patel_2003,Caporaso_2009,Odette_2005,2005}. \cite{Komarov_2013,Patel_2003,Caporaso_2009,Odette_2005}.  When a fast ion moves through a solid, it loses kinetic energy due to the excitations of the target electrons and the path of their trajectory.   This energy-loss phenomenon plays an important role in many experimental studies involving solids, surfaces and nanostructures. nanostructures [add citation].  The complexity of describing the dynamic interaction between charged particles and solids has initiated a large amount of research both experimentally and theoretically in recent years; in the latter the condensed matter community, however, have initiated sophisticated computer simulation techniques with considerable success.   Among the many measurable quantity the stopping power $\mathrm(S)$ \cite{Ferrell_1977} has received much attention; it provided detailed information regarding the energy transfer between the incoming projectile and the solid target.   The theoretical models employed to study stopping of elementary charged particles in solids \cite{Bloch_1933,Bethe_1930} has stimulated this kind of study.  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 targetbound  electrons to the projectile ions. 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.