Stopping power and phase shift for slow ions in an electron gas

The results of the stopping power and the Fermi – level phase shifts are presented for slow ions moving with velocity smaller than Fermi velocity in an electron gas. The calculations are made based on nonlinear density functional theory (DFT). For slow ion the interaction of the ion – electron gas occurs via scattering at the Fermi surface and can be codified in phase shifts at the Fermi energy leading to scattering cross sections and energy loss. The phase shift was computed using the single particle wave functions using the density functional method. The single particle wave functions are used to calculate the ground – state density of the electron. Further,nonlinear – phase shift results of stopping power are also calculated in classical and quantum mechanics taking into consideration the effective charge.