  The ionization of a hydrogen-like heavy ion by impact of a charged projectile
under simultaneous irradiation by a short laser pulse is investigated within
the non-perturbative approach, based on numerical solutions of the
time-dependent Dirac equation. Special emphasis is placed on the question of
whether the laser- and impact-ionization channels interfere with each other,
and how this intereference affects the ionization probability. To answer this
question we performed detailed calculations for the laser-assisted collisions
between hydrogen-like $Pb^{81+}$ and alpha particles. The results of the
calculations clearly indicate that for the experimentally relevant set of
(collision and laser) parameters, the interference contribution can reach 10%
and can be easily controlled by varying the laser frequency.
