| This dissertation consists of three parts. In the first part, the effect of the large impact parameter near-elastic peak of collisional energy transfer for unimolecular dissociation/bimolecular recombination reactions and deviation from equilibrium case is studied. To this end the conventional single exponential model, a bi-exponential model that fits the literature classical trajectory data better, a model with a singularity at zero energy transfer, and the most realistic model, a model with a near-singularity, are fitted to the trajectory data in the literature. A theory is developed for the population distribution as a function of the energy E of a dissociating model, and used to calculate the three-body low pressure recombination rate constant. In the second part, the electron transfer process in the single quantum dot fluorescence blinking phenomenon is studied. The DCET (diffusion controlled electron transfer) model has been modified to explain the exponential cutoff of the power law time distribution of the bright state and the quadratic dependence of the exponential tail on the excitation intensity. Based on ensemble measurements it is proposed that an exponential tail for the dark state time distribution for long time experiments exists for single trajectory experiments. In the last part, we develop a general MLE (maximum likelihood estimation) method to analyze experimental data with a potential distribution of power law form which can be extended to a power law with an exponential tail and more generally, many other distribution forms. |
