On the approximation of independent pairs in diffusion kinetics: correlation of distances in a three-body system

This study investigates the problem of diffusion kinetics in a three-body system, motivated by the theory of radiation chemical kinetics. The backward diffusion equation for the joint density of the distances is formulated, and an explicit formula for the infinitesimal covariance of two diffusing distances is derived. The Clifford-Green theorem is used to show how the infinitesimal covariance of two distances is linked to the covariance of the corresponding two squared distances as time evolves. In addition, computer simulations for the problem are presented, which indicate that hitting probabilities are also correlated. While the results indicate that more work is needed before a usable correction to the independence approximation is possible, clear progress has been made.