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Alfredo A. Correa edited Among_the_measurable_quantities_associated__.tex
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Among the measurable quantities associated to the interaction between ions and solid, 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.
Various models and theories have been proposed to calculate stopping cross sections; even today a unified \emph{ab initio} 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 few reviews (\cite{Race_2010} and references there in).
Recently, from a phenomenological point of view, Uddin {\emph et al.} \cite{Alfaz_Uddin_2013} have calculated $S$ for various media with atomic number $Z=2$ to $100$ using realistic electron density with four fitted parameters and obtained $\sim 15\%$ agreement with the \textsc{Srim} data \cite{Ziegler_2010}. Using a single formula with fewer parameters Haque {\emph et al.} \cite{Haque_2015} have reported proton impact $\mathrm{SCS}$ with encouraging results.
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.