where 0(v) is the velocity distribution, normalized such that /O°0(v)dv = 1 (Appendix C.6.2). This expression only applies if particles "a" and "X" are of a different kind. In this case, nanX is the number of interacting pairs of particles. If the particles are of the same sort, e.g., if particles "a" interact with other particles "a", the number of interacting pairs is (1/2) na (na - 1) = (1/2) n^, since the interaction of two particles must be counted only once. Thus, a more general writing of (9.5) is nanX AaX - ^ ,„ ,, raX = n , g s , with AaX =< av , (9.6)
where 5aX is Kronecker's symbol (¿ax = 1, if a=X; 5aX = 0, if a=X). AaX is the reaction rate by pair of particles. In thermodynamic equilibrium, the relative velocities v of particles of masses mi and m2 with a reduced mred = mi m2/(mi + m2) also follows the Maxwell-Boltzmann distribution (C.62)
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