  The paper explores the shadow of the repulsive Rutherford scattering - the
portion of space entirely shielded from admitting any particle trajectory. The
geometric properties of the projectile shadow are analyzed in detail in the
fixed-target frame as well as in the center-of-mass frame, where both the
charged projectile and the charged target cast their own respective shadows. In
both frames the shadow is found to take an extremely simple, paraboloidal
shape. In the fixed-target frame the target is precisely at the focus of this
paraboloidal shape, while the focal points of the projectile and target shadows
in the center-of-mass frame coincide. In the fixed-target frame the shadow
takes on a universal form, independent of the underlying physical parameters,
when expressed in properly scaled coordinates, thus revealing a natural length
scale to the Rutherford scattering.
