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\section{Introduction}  The study of the 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}\cite{Patel_2003}\cite{Caporaso_2009}\cite{Odette_2005}. applications\cite{Komarov_2013}\cite{Patel_2003}\cite{Caporaso_2009}\cite{Odette_2005}\cite{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 phenomenon 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 large amount of research both experimentally and and theoretically; in the latter the condensed matter community have initiated sophisticated computer simulation techniques with great success.