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\section{Introduction}  The study of the interaction of charged particles with matter has been a subject of extensive research for many years and represents an important quantity for many technological applications such as nuclear safety, applied material science, medical physics and fusion and fission applications. applications\cite{Komarov_2013}\cite{Patel_2003}\cite{Caporaso_2009}\cite{Odette_2005}.  When a slow ion moves through a solid, they lose kinetic energy due to the electronic excitations of the target electrons and the path of their trajectory.