  In order to discern aggregation in solutions, we present a quantum mechanical
analog of the photon statistics from fluorescent molecules diffusing through a
focused beam. A generating functional is developed to fully describe the
experimental physical system as well as the statistics. Histograms of the
measured time delay between photon counts are fit by an analytical solution
describing the static as well as diffusing regimes. To determine empirical
fitting parameters, fluorescence correlation spectroscopy is used in parallel
to the photon counting. For expedient analysis, we find that the distribution's
deviation from a single Poisson shows a difference between two single fluor
moments or a double fluor aggregate of the same total intensities. Initial
studies were performed on fixed-state aggregates limited to dimerization.
However preliminary results on reactive species suggest that the method can be
used to characterize any aggregating system.
