RATE-EQUATION OF THE A+A-]A REACTION WITH PROBABILITY OF REACTION AND DIFFUSION

We study the coagulation reaction A + A --> A with probability p of reaction in a one-dimensional lattice. We show that drho/dt = -pGAMMA1, where rho(t) is the density of particles and GAMMA1(t) is the density of nearest-neighbor occupied sites. From the analysis of the crossover between the reaction-controlled-reaction and the diffusion-controlled-reaction regimes an approximate scaling ansatz for GAMMA1 and rho for different values of p is proposed. Using this scaling, the collapse of Monte Carlo data improves when p decreases. From this scaling an analytical approximation of the density is found which agrees well with the numerical results of rho(t) for different values of p.