Suna's kinematic equations describing exciton annihilation in aromatic crystals are solved for higher exciton densities $n$, i.e., where $n\ge \frac{\beta }{\gamma }$, where $\beta$ is the monomolecular decay rate and $\gamma$ is the bimolecular annihilation rate constant. It is found that in case of diffusion-limited annihilation, $\gamma$ is a function of the exciton density $n$ even for $n$ small compared to the lattice site density. In general $\gamma$ is then a monotonically increasing function of $n$ and these density effects depend on the dimensionality of the exciton motion. For both triplet and singlet excitons, $\gamma$ is a function of $n$ in one-dimensional and two-dimensional systems only. In the case of singlet excitions, $\gamma$ depends on $n$ even in three-dimensional systems if reabsorption is a dominant mechanism of exciton motion. Some materials are suggested in which such effects could be experimentally observable.

• Received 14 November 1978

DOI:https://doi.org/10.1103/PhysRevB.19.5206