 
Summary: 16548 Phys. Chem. Chem. Phys., 2011, 13, 1654816557 This journal is c the Owner Societies 2011
Cite this: Phys. Chem. Chem. Phys., 2011, 13, 1654816557
The residence probability: single molecule fluorescence correlation
spectroscopy and reversible geminate recombination
Noam Agmon*
Received 24th March 2011, Accepted 28th June 2011
DOI: 10.1039/c1cp20907h
The residence probability of a freely diffusing particle within an open ddimensional ball is
calculated as a function of time, for an initial distribution that is either a spherical delta function
or uniform within the sphere. The latter is equivalent to the autocorrelation function (ACF) of
fluorescence correlation spectroscopy (FCS) when utilizing nearfield scanning optical microscopy
(NSOM) probes. Starting from the general equation for the Laplace transform of the residence
probability, we solve it in Laplace space for any dimensionality, inverting it into the time domain
in one and threedimensions. The short and longtime asymptotic behaviors of the residence
probability are derived and compared with the exact results. Approximations for the two
dimensional ACF are discussed, and a new approximation is derived for the NSOMFCS ACF.
Also of interest is an analytic expression for a threedimensional ACF, which could be useful for
twophoton FCS. Analogy with the binding probability for reversible geminate recombination
suggests that more information could be extracted from the longtime tails in FCS experiments.
1 Introduction
