We have experimentally tested a recently suggested possibility for anomalous sensitivity of the cross sections of dissipative heavy ion collisions. Cross sections for the $^{19}$F+$^{27}$Al dissipative collisions were measured at the fixed energy 118.75 MeV of the $^{19}$F for the 12 different beam spots on the same target foil. The data demonstrate dramatic differences between the cross sections for the different beam spots. The effect may indicate deterministic randomness in complex quantum collisions. New experiments are highly desirable in a view of the fundamental importance of the problem.
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