  This work addresses nucleation rates in systems with strong initial
recombination. Initial (or `geminate') recombination is a process where a
dissociated structure (anion, vortex, kink etc.) recombines with its twin
brother (cation, anti-vortex, anti-kink) generated in the same nucleation
event. Initial recombination is important if there is an asymptotically
vanishing interaction force instead of a generic saddle-type activation
barrier. At low temperatures, initial recombination strongly dominates
homogeneous recombination. In a first part, we discuss the effect in one-,
two-, and three-dimensional diffusion controlled systems with spherical
symmetry. Since there is no well-defined saddle, we introduce a threshold which
is to some extent arbitrary but which is restricted by physically reasonable
conditions. We show that the dependence of the nucleation rate on the specific
choice of this threshold is strongest for one-dimensional systems and decreases
in higher dimensions. We discuss also the influence of a weak driving force and
show that the transport current is directly determined by the imbalance of the
activation rate in the direction of the field and the rate against this
direction. In a second part, we apply the results to the overdamped sine-Gordon
system at equilibrium. It turns out that diffusive initial recombination is the
essential mechanism which governs the equilibrium kink nucleation rate. We
emphasize analogies between the single particle problem with initial
recombination and the multi-dimensional kink-antikink nucleation problem.
