The Bohr theory treats charged-particle stopping as a sequence of interacti
ons with classical target electrons bound harmonically to their equilibrium
positions. We demonstrate that equivalent results can be derived on the as
sumption of free binary collisions governed by a suitable effective potenti
al. This kind of mapping is rigorous in the limits of distant and close col
lisions and therefore provides a tool to evaluate energy losses via binary-
scattering theory. This model was developed with the aim of calculating sto
pping forces for heavy ions at moderately high velocities, where a classica
l-orbital calculation is typically superior to the Born approximation. The
effective potential employed holds equally well for dressed as for stripped
ions. Unlike the Bohr theory, the present evaluation avoids a formal divis
ion into regimes of close and distant collisions that do not necessarily jo
in smoothly. Moreover, no perturbation expansion is necessary. For these re
asons the overall accuracy as well as the range of validity of the Bohr mod
el are significantly enhanced. Extensive tests have been performed, includi
ng comparisons with rigorous evaluations of the Z(1)(3) effect, with excell
ent agreement even where such was not necessarily expected. Moreover, credi
ble results have been obtained under conditions where the perturbation expa
nsion shows poor convergence. A comparison with experimental data on O-Al i
s encouraging, even though shell corrections and projectile excitation/ioni
zation have not yet been incorporated and input has not yet been optimized.