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Since vo divided by some standard volume is the flux of incident systems, and since If,,(O,#) 1% divided by the same standard volume is the flux of scattered systems per unit solid angle with the quantum numbers ( I Z , ~ then ), the cross-section of Eq. (161)is associated with the probability of transition per unit solid angle from a specific incident initial state with quantum numbers (1,m) to any one of the scattered final states (n,$) within a specified wave number or energy range. Again, the same formulas may be gleaned from the time-dependent perturbation theory.

112c) is reduced to + ( K , Y - W,)g = 0 (114) where KAvis K , with N equal to c. lB The procedure, however, is rather complicated and is usually not employed, largely because of the degeneracy in the rotational states, which causes the wave function g not to be separable directly as a product, but as a sum of products. B. First-Order Approximations (1) First-Order Time-Dependent Perturbation Theory23 Substitution of Eq. (4) in Eq. (I), also utilizing Eq. , which is any one of y;, and integration over all space, leads t o ihbfe-iw;t/fi= > , e - i W A h 3 1y ?

For the sake of clarity we mention here that in the later discussion there are two different processes through which the system seeks equilibrium. We stress, of course, the chemical reaction process leading the system to chemical equilibrium. But at the same time the reactants and products themselves seek equilibrium in their internal and translational states. For simplicity, it is sometimes assumed that the reactants are in an equilibrium distribution during the approach to chemical equilibrium.

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ADVANCES IN CHEMICAL PHYSICS VOLUME 6 by I. PRIGOGINE


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