  The dynamics of electrons in the presence of a positive ion is considered for
conditions of weak electron-electron couping but strong electron-ion coupling.
The equilibrium electron density and electric field time correlation functions
are evaluated for semi-classical conditions using a classical statistical
mechanics with a regularized electron-ion interaction for MD simulation. The
theoretical analysis for the equilibrium state is obtained from the
corresponding nonlinear Vlasov equation. Time correlation functions for the
electrons are determined from the linearized Vlasov equation. The resulting
electron dynamics is described in terms of a distribution of single
electron-ion trajectories screened by an inhomogeneous electron gas dielectric
function. The results are applied to calculation of the autocorrelation
function for the electron electric field at the ion for $ 0\leq Z\leq 40$,
including conditions of strong electron-ion coupling. The electron stopping
power and self-diffusion coefficient are determined from these results, and all
properties calculated are compared with those obtained from semi-classical
molecular dynamics simulation. The agreement with semi-classical MD simulation
is found to be reasonable. The theoretical description provides an instructive
interpretation for the strong electron-ion results.
