  Barrier crossing calculations in chemical reaction-rate theory typically
assume that the barrier is large compared to the temperature. When the barrier
vanishes, however, there is a qualitative change in behavior. Instead of
crossing a barrier, particles slide down a sloping potential. We formulate a
renormalization group description of this noisy saddle-node transition. We
derive the universal scaling behavior and corrections to scaling for the mean
escape time in overdamped systems with arbitrary barrier height. We also
develop an accurate approximation to the full distribution of barrier escape
times by approximating the eigenvalues of the Fokker-Plank operator as equally
spaced. This lets us derive a family of distributions that captures the barrier
crossing times for arbitrary barrier height. Our critical theory draws links
between barrier crossing in chemistry, the renormalization group, and
bifurcation theory.
