THE ONE-DIMENSIONAL LORENTZ GAS - A MODEL FOR GEMINATE RECOMBINATION REACTIONS

In order to gain insight into the phenomenon of the solvent cage effec t, which plays an important role in the dynamics of geminate recombina tion reactions, we present some studies on a simplified model - the on e dimensional Lorentz gas. In this model fixed, point scatterers are p laced at random along a line and a single point particle moves amongst them. On colliding, the traveller may be reflected or transmitted wit h a certain probability. We use computer simulation to calculate the v elocity correlation function (VCF) and the distribution of first retur n times to a given scatterer (J(t)) for three reflection probabilities . We also consider an approximate theory, whereby the traveller rememb ers, after every collision, the position of the previous scatterer and the fact that there is a region of free space between the last and th e present scatterer. This theory correctly predicts there to be a nega tive well in the VCF but underestimates its magnitude. For the first-r eturn time problem, however, it gives very good agreement with the ful l simulation results. We also analyse the short and long time behaviou r of J(t) and compare with predictions from the Lorentz- Boltzmann equ ation.