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Among the measurable quantities associated to the interaction between ions and solids, the stopping power $\mathrm(S)$ \cite{Ferrell_1977} has received much attention; it provides information regarding the energy transfer between the incoming projectile and the solid target.  When a fast ion moves through a material, it loses most of its kinetic energy due to the excitations of the  target electrons along its trajectory  in what constitutes a fundamentally non-adiabatic process. This energy-loss phenomenon plays an important role in many experimental studies involving radiation in solids, surfaces, and nanostructures \cite{Chenakin_2006,Figueroa_2007,Markin_2008,Kaminsky_1965,Lehmann_1978,Sigmund_2014,Nastasi_1996}.   Various models and theories have been proposed to calculate stopping cross sections due to electrons.