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Edwin E. Quashie edited section_Introduction_The_interaction_of__.tex
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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.
Varies models and theories have been proposed to calculate stopping cross sections ($\mathrm{SCS}$); even today a unified theoretical approach suitable for different projectiles and energies is not available in the literature. Employing the First Born Approximation (FBA), Bethe \cite{Bethe_1930_EN} has reported the calculation of inelastic and ionization cross section. The Bloch correction \cite{Bloch_1933} provides a convenient link between the Bohr and the Bethe scheme. Fermi and Teller \cite{Fermi_1947} using electron gas models had reported electronic stopping for various targets. The Bethe formula for stopping has been studied in details by Lindhard and Winther \cite{Lindhard_Winther} on the basis of the generalized linear-response theory. All these models require ad-hoc assumptions for studying stopping processes. For calculating electronic stopping in metals there are a few reviews
\cite{Race_2010,ref. there in} \cite{Race_2010} show theoretical progress and we not repeating them here.
The development of time dependent density functional theory (TDDFT) \cite{Runge_1984} enhanced the diverse study of many body problems involving the slowing down of charged projectiles in metals. It has enjoyed much consideration owing to its electron dynamics both self-consistency and non-perturbative way \cite{Kohn_1965}.