Long-range recombination of immobile particles

He kills the matter and then says that it is dead. 

Let us illustrate an analysis of the accuracy of the superposition approximation presented in Section 5.1 by both numerical calculations and analytical estimates. Following [1], in Figs 6.1 and 6.2 a solution of a set of equations (4.1.19), (4.1.28), (6.1.14) to (6.1.16) is presented for different choices of parameters assuming that particle concentrations are equal = riB t) = n t). 

It is well seen from Fig. 6.1 that the reaction rate in systems with greater space dimension d is also accelerated. It results from the fact that if d increases, a number of AB pairs separated by a given distance also does so. The asymptotic behaviour of n(f) as t — oo depends also on d and needs a special analysis. 

In its turn Fig. 6.2 illustrates the effect of the initial concentration on the static tunnelling recombination kinetics. The latter is defined by a competition of three distinctive scales - the tunnelling recombination radius ro, mean distance between particles Iq = 71(0) / and lastly, the time-dependent correlation radius At long time curves corresponding to different initial concentrations could be coincided by their displacements along ordinate axis, which confirms existence of the universal asymptotic decay law. 

The correlation functions plotted in Figs 5.5 and 5.6 present the statistical information about relative spatial distribution of reacting particles. In particular, the distinctive scale emerges here, thus indicating that all dissimilar 

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

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