EXACT SOLUTION OF 2-SPECIES BALLISTIC ANNIHILATION WITH GENERAL PAIR-REACTION PROBABILITY

The reaction process A + B --> <empty set> is modelled for ballistic r eactants on an infinite line with particle velocities upsilon(A) = c a nd upsilon(B) = -c and initially segregated conditions, i.e., all A pa rticles to the left and all B particles to the right of the origin. Pr evious models of ballistic annihilation have particles that always rea ct on contact, i.e., pair-reaction probability p = 1. The evolutions o f such systems are wholly determined by the initial distributions of p articles and therefore do not have a stochastic dynamics. However, in this paper the generalization is made to p less than or equal to 1, al lowing particles to pass through each other without necessarily reacti ng. In this way, the A and B particle domains overlap to form a fluctu ating, finite-sized reaction zone where the product <empty set> is cre ated. Fluctuations are also included in the currents of A and B partic les entering the overlap region, thereby inducing a stochastic motion of the reaction zone as a whole. These two types of fluctuations, in t he reactions and particle currents, are characterised by the intrinsic reaction rate, seen in a single system, and the extrinsic reaction ra te, seen in an average over many systems. The intrinsic and extrinsic behaviors are examined and compared to the case of isotropically diffu sing reactants.