Statistical behavior of elementary collinear exchange reactions A+BC→AB+C

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Abstract
In this paper, we revisit the analysis of the classical statistical behavior of three‐atom collinear exchange reactions A+BC→AB+C. We begin with the intuitive reason why the statistical assumption (all the states of the available phase space are equiprobable) can, a priori, be applied without any restriction to a collisional process. To check the validity of this hypothesis, we show that an extention of the method of Wagner and Parks allows one to compute the statistical distributions of recoil energy for reactions involving a long lifetime intermediate complex. A comparison between these numerical distributions and the theoretical ones leads to some discrepancies. In order to understand the origin of these unexpected results, we implement a numerical experiment showing that trajectories ‘‘lose the memory’’ of their initial conditions in a reduced area of the region where the three atoms interact. As a consequence, the statistical assumption is only applied in this area which we call the statistical region. The agreement between the resulting theoretical distributions and the numerical ones is now very satisfactory. Thus, the statistical assumption defined above fails. This surprising result shows the originality of the statistical behavior of unbounded systems with a few degrees of freedom, as compared with the larger systems usually treated by statistical mechanics.