Surface Integral Form for Three-Body Collision in the Boltzmann Equation

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Abstract
A new form is given for the triple-collision term in the generalized Boltzmann equation which is more similar to the well-known binary-collision expression than those given heretofore. The form involved is a surface integral over a five-collision parameter space which is the generalization of the two-dimensional collision parameter space for binary collisions. For "soft" repulsive interactions, the expression involves both the asymptotic properties of three-body collisions before and after the collision, and the dynamics of binary collisions during the collision process. For hard spheres, the expression involves only the asymptotic properties of ternary and binary collisions.