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\section{Introduction}  The study of the interaction of charged particles with matter has been a subject of extensive research over last few 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}\cite{Patel_2003}\cite{Caporaso_2009}\cite{Odette_2005}. When a slow ion moves through a solid, it loses kinetic energy due to the electronic excitations of the target electrons and the path of their trajectory. This is an important phenomenon which plays an important role in many experimental studies involving solids, surfaces and nanostructures. The complexity of describing the dynamic interaction between charged particles and solids has initiated a gargantuan amount of research both experimentally and and theoretically; in the latter the condensed matter community have initiated sophisticated computer simulation techniques with great success. Among the many measurable quantity the stopping power $\mathrm(S)$\cite{Ferrell_1977} has enjoyed much uses; it provided details 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}\cite{Bethe_1930}, has simulated this kind of study.  The stopping power depends heavily on the incident  velocity of an atomic projectile characterizes its the projectile, in conformity with the earlier observation of the Firsov model [6) and the Lindhard electron-gas theory\ref{Lindhard_1961}\ref{Sugiyama_1981} [7], where they have shown that the  stopping power in has  a given solid target. linear dependency on the projectiles velocity.  The type of excitation created in the solid target describes the stopping phenomenon produced. When the velocity of the projectile is high, the host nuclei barely have enough time to interact with the charged particle hence less energy or momentum is transfered. The main channel of energy dissipation in this case is caused by the electrons around the trajectory of the charged particle hence electronic excitations are predominant. Also in higher velocity regime, the electronic curve has a maximum, which is due to the limited response time of electrons to the atomic projectile. In the other hand, if the velocity of the charged particle is low, the stopping power is predominantly caused by nuclear effects due to lattice excitations in the host nuclei. In recent times, the development of time-dependent methods has opened new ways in describing slowing down of charged projectiles in matter theoretically. Time-dependent density functional theory (TDDFT) especially provides non-perturbative and self-consistent treatment of electron dynamics in many body systems.[put more paper references here]. 
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