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Theoretical calculations, applying elements of the orbital-based densityfunctional method for self-consistent screening in an electron gas to thestopping power of metals for slow projectiles are reviewed, by focusing ondifferences in modelings. New, two-channel-based results on the averageretarding force are presented. All theoretical results are compared withpioneering experimental data, obtained for carbon target, on $Z_1$-oscillationin stopping at random collisional condition.

$Z_1$-oscillation in the retarding force of metals for slow ions: Comparative study of theoretical modelings