Hard-core potential reactions

Let US consider an isolated pair of reactants A and B whose positions in space are r and re at time t. For simplicity, these reactants will be taken as uncharged and there is no potential of mean force consideration to be included either. Such factors may always be included later. The probability that species A is in the small volume cIta at r and species B is in the small volume drg at rg at time t is n rp, r, t) dr drs- Both species can diffuse independently of one another. They can even diffuse through each other, in principle, though in practice this is improbable because A and B will react before they b in to pass through each other. This can always be prevented by including a hard core repulsive term in the interaction evergy, U, which tums-on just inside the reaction distance, R. The probability density rs, t) can change with time due to diffusion of either A or B or both species. The rate of loss of A from is and, similarly, the loss of B from tg is D V n. In these terms, the subscript A and B refer to the co-ordinates of A or B, respectively, and the diffusion coefficients of A and B are, respectively, I>a The dif-... 

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