Exact solution of homogeneous ballistic annihilation with a general reaction probability

The homogeneous single-species A + A (p) under right arrow 0 reaction with ballistic reactants and a binary-velocity distribution is solved in the case of equal initial densities of particles with positive and negative velocities. Previous studies have considered the model when the pair reaction probability, p, is one. Here the long-time behaviour of the density decay is solved exactly in one dimension for general p. It is shown that, in contrast to recent numerical studies, the decay of the density at long times is a universal quantity independent of the reaction probability.