AN OPTIMAL NUMERICAL-SOLUTION OF DIFFUSIONAL RECOMBINATION PROBLEMS

The Smoluchowski equation used to describe recombination of particles that undergo diffusive motion is traditionally solved numerically by truncating the region of interparticle distances and employing a varying discretization which is manually adjusted according to the form of the interparticle interaction and the problem to be solved. By using a transformed quantity as independent variable rather than the interparticle distance it is possible to cover the complete region of space and to use an equidistant discretization that is automatically optimal for the given interaction. Furthermore by transforming the equation into a self-adjoint form and using the backward equation the recombination probability can be calculated directly for all initial distributions at once. This implies that the bulk recombination or the rate constant is obtained simultaneously. The method has a controllable accuracy and it is applied to a calculation of the time independent limiting quantities and the Laplace transformed solutions.