  Rutherford scattering is usually described by treating the projectile either
classically or as quantum mechanical plane waves. Here we treat them as wave
packets and study their head-on collisions with the stationary target nuclei.
We simulate the quantum dynamics of this one-dimensional system and study
deviations of the average quantum solution from the classical one. These
deviations are traced back to the convexity properties of Coulomb potential.
Finally, we sketch how these theoretical findings could be tested in
experiments looking for the onset of nuclear reactions.
