General solution for the arbitrary hopping length

To treat the problem of recombination kinetics for arbitrary hopping lengths 0 A oo, it is convenient to restrict ourselves to the exponential hopping length distribution known as the Torrey model [82]. In this particular case the integral kernel (r, r ) which in equation (4.3.5) is defined by distribution results in 

Depending on Ao, this half plane is divided vertically into three regions - diffusion, intermediate and hopping. For the first two regimes one can simplify equation (4.3.21) putting there G = 0, thus getting 

On the other hand, when approaching the intermediate region from the hopping side (large x), the following estimate was derived  

To understand an effect of A upon the kinetics, it is useful to consider the cross-section D = XqTq = const. It could be shown that at large ( the approximations (4.3.22) and (4.3.23) overlap in the intermediate region. Con- 

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