The cross-over between diffusion-limited and reaction-limited cooperative behaviour in reaction-diffusion systems
is studied through the change of the scaling behaviour of the coagulation-diffusion process.
This model is exactly solvable through the empty-interval method, which can be extended from the chain to the
Bethe lattice, in the ben-Avraham-Glasser approximation. On the Bethe lattice, an analysis of a stochastic reset
to a configuration of uncorrelated particles reveals in the stationary state logarithmic corrections to scaling, as expected for
systems at the upper critical dimension. Analogous results hold true for the time-integrated particle-density.
The cross-over scaling functions and the associated effective exponents are derived.