In laser-induced collisions between ultracold atoms, the combination o
f low velocities and long-range interactions results in collision time
s which can exceed the excited-state lifetime. We use a cooperative ef
fect between two lasers to explicitly observe this time dependence. Th
e first laser, tuned near resonance, excites the atom pair at long ran
ge and enhances the collisional flux available for short-range excitat
ion by a second, far-detuned laser. Using pulsed excitation, we find t
his collisional process to take place on a 10(-6) s time scale, in rea
sonable agreement with trajectory simulations. [S0031-9007(97)05219-8]
.