Alfredo A. Correa edited section_Introduction_The_interaction_of__.tex  over 8 years ago

Commit id: 96d130599ba06c6021115690d033a23b002f8ac6

deletions | additions      

       

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}.   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 themany  measurable quantity 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. Varies Various  models and theories have been proposed to calculate stopping cross sections ($\mathrm{SCS}$); 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} (\cite{Race_2010}  and ref. references  there in\} show theoretical progress and we not repeating them here. in).  The development of time dependent density functional theory (TDDFT) \cite{Runge_1984} enhanced the diverse study of many body problems. problems and in particular the problem at hand.  It has enjoyed much consideration owing to its electron dynamics both self-consistency and non-perturbative way \cite{Kohn_1965}. In studying the role of radiation damage in $\mathrm{H^+ + Al}$ interactions Correa {\emph et al} \cite{Correa_2012} have shown that the electronic excitations due to molecular dynamics (MD) are quite different from the adiabatic outcome. Even today the inclusion of non adiabatic effects in a real calculation poses a challenging problem. Recently Schleife {\emph et al} \cite{Schleife_2015} have calculated the electronic stopping $\mathrm(S_\text{e})$ by $\mathrm{H}$ and $\mathrm{He}$ projectile including non-adiabatic interactions and found that off-channeling trajectories along with the inclusion of semicore electrons enhance $\mathrm{S_\text{e}}$ resulting better agreement with the experiment. Recently Uddin {\emph et al.} \cite{Alfaz_Uddin_2013} have calculated $\mathrm{SCS}$ 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.