The correct prediction of the electronic stopping power is important in establishing the basis for the technique of ion bombardment of neutron damage. Experimental measurements of the stopping power and the depth distribution of damage deposition by heavy atomic projectiles incident on matter have shown that the velocity proportional electronic stopping power formulas of Lindhard and Firsov are not valid for projectile velocities in the range from 2v0up tov1, wherev0is the Bohr velocity andv1is Lindhard’s proposed upper limit for the validity of these formulas. This letter points out that a previously published modification of the Firsov theory predicts a strong superlinear dependence of the stopping power on velocity in this velocity region due to effects which arise when the incident projectile velocity is comparable with that of the atomic electrons. Apart from a scale factor along the velocity axis, which must be determined from experimental measurement, the modified theory correctly predicts the energy dependence of the low‐energy electronic stopping power. Values of the scale factor for a large collection of projectile‐target combinations indicate that for most projectile‐target combinations the velocity‐proportional region of the electronic stopping power does not extend abovev0.