STATISTICAL BEHAVIOR OF ELEMENTARY COLLINEAR EXCHANGE-REACTIONS A-]AB+C(BC)

In this paper, we revisit the analysis of the classical statistical be havior of three-atom collinear exchange reactions A+BC --> AB+C. We be gin with the intuitive reason why the statistical assumption (all the states of the available phase space are equiprobable) can, a priori, b e applied without any restriction to a collisional process. To check t he validity of this hypothesis, we show that an extention of the metho d of Wagner and Parks allows one to compute the statistical distributi ons of recoil energy for reactions involving a long lifetime intermedi ate complex. A comparison between these numerical distributions and th e theoretical ones leads to some discrepancies. In order to understand the origin of these unexpected results, we implement a numerical expe riment showing that trajectories ''lose the memory'' of their initial conditions in a reduced area of the region where the three atoms inter act. As a consequence, the statistical assumption is only applied in t his area which we call the statistical region. The agreement between t he resulting theoretical distributions and the numerical ones is now v ery satisfactory. Thus, the statistical assumption defined above fails . This surprising result shows the originality of the statistical beha vior of unbounded systems with a few degrees of freedom, as compared w ith the larger systems usually treated by statistical mechanics.