  In reaction-diffusion models of annihilation reactions in low dimensions,
single-particle dynamics provides a bottleneck for reactions, leading to an
anomalously slow approach to the empty state. Here, we construct a reaction
model with a reciprocal bottleneck on particle dynamics where single-particle
motion conserves the center of mass. We show that such a constrained
reaction-diffusion dynamics does not approach an empty state but freezes at
late times in a state with fragmented particle clusters, and that the late-time
dynamics and asymptotic density are universal. Our setup thus constitutes a
minimal model for the fragmentation of a one-dimensional lattice into
independent particle clusters, and we provide exact results for the final
density in the large-reaction rate limit. We suggest that the universal
reaction dynamics could be observable in experiments with cold atoms or in the
Auger recombination of exciton gases.
