Recombination of immobile reactants

In the case of long-range recombination of immobile particles ( = 0) occurring at a low temperature, we can use equation (4.1.23) to obtain 

The integral entering equations (4.1.25) and (4.1.27) could easily be expressed as 

Therefore, the universal asymptotic decay kinetics are for equal concentrations 

The actual time behaviour of F t), shown in equation (4.1.41), depends on the choice of cr r). This quantity F t) could be presented in a more universal and transparent form in terms of the correlation length Let us consider as an illustration the multipole interaction which is observed in many solids and liquids due to the interaction of the electronically excited donors D with acceptors A resulting in an energy transfer D + A D + A + A + hu [16, 17]. Its probability (per unit time) is 

The case m — 6 corresponds to the most long-range dipole-dipole interaction. Define how the time-dependent correlation length (subscript 0 indicates that the linear approximation is employed)  

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