Escape of particles from a local cluster

The radiation chemical spur contains a number of radicals and/or ions in a cluster. It was discussed in some detail in Chap. 7, Sect. 4. However, because the theoretical framework has not been presented in much detail before [437, 503, 504], a brief account is given here. 

A necessary consequence of choosing a complex systems to study is the rather ciumsy notation required to specify adequately what is being described mathematically it is, in one sense, little more than bookkeeping Take M cations located at p °, p2°.., pM° = p0 and which are stationary and N anions initially located at rj°, r2°. rjV° = r0 at a time, t°. At a later time, t, the anions have diffused to r. The initial distribution of anions is 

To extend this analysis further to include the cations as well as anions, all that is required is to use the density nNtM and the potential energy UNrM. Rather than represent reaction by a boundary condition, there is much advantage using the Wilemski and Fixman approach of sink terms [ 51 ]. Let the anion and cation p react when they overlap in the region, say, where i r, — p j = R, and specify it by iix — 5 (i — jry — p i). The rate of 

Such a reaction leads to the loss of the probability that all N anions and M cations are present and 

When the anion k and cation v react, the density of N anions and M cations becomes zero and a distribution containing N — 1 anions (but not anion k) and M cations (but not cation v) is formed. The rate of formation of the IV —1, M — 1 density is Kcifdak j ihl,nNiM and so the diffusion equation for this density is [503] 

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