  Ballistic injection in a nanodevice is a complex process where electrons can
either be transmitted or reflected, thereby introducing deviations from the
otherwise quantized conductance. In this context, quantum rings (QRs) appear as
model geometries: in a semiclassical view, most electrons bounce against the
central QR antidot, which strongly reduces injection efficiency. Thanks to an
analogy with Rutherford scattering, we show that a local partial depletion of
the QR close to the edge of the antidot can counter-intuitively ease ballistic
electron injection. On the contrary, local charge accumulation can focus the
semi-classical trajectories on the hard-wall potential and strongly enhance
reflection back to the lead. Scanning gate experiments on a ballistic QR, and
simulations of the conductance of the same device are consistent, and agree to
show that the effect is directly proportional to the ratio between the strength
of the perturbation and the Fermi energy. Our observation surprisingly fits the
simple Rutherford formalism in two-dimensions in the classical limit.
