  Theoretical calculations, applying elements of the orbital-based density
functional method for self-consistent screening in an electron gas to the
stopping power of metals for slow projectiles are reviewed, by focusing on
differences in modelings. New, two-channel-based results on the average
retarding force are presented. All theoretical results are compared with
pioneering experimental data, obtained for carbon target, on $Z_1$-oscillation
in stopping at random collisional condition.
