Abstract
The reaction-rate theory plays a prominent role in many applications to physical and chemical phenomena. The classical transition state theory for calculating complex dissociation rates requires separation of time scales. We consider particle-trap complexes with long-range interaction and, hence, non-exponential distribution of dissociation times, for which the conventional rate equations cannot be applied. We show that the deviation from the exponential law is due to particles that re-cross the dividing surface without reaching regions of the well deeper than the thermal energy. The concentration of complexes is determined by a small fraction of all particles that reach sites with high binding energy. As a result, it obeys the first-order reaction kinetics with a rescaled mean dissociation time and cross-section of complex formation.
