State specific rate constant quantum calculations

Reaction rate constants cannot be used to describe such detailed processes. Instead the differential reaction cross section, areact ( i, 2, 3, n l, 2 0 ployed, where n, are various quantum numbers and the primed quantities refer to reaction products. Such cross sections represent the effective collision area for reagents with given i, 2, , to give specific products. Rate constants represent the effective average of the product of the cross section with the approach velocity taken over the calculated distribution of reagent quantum states. 

Although equation (3) provides a rigorous quantum definition of the cumulative reaction probability - and thus the canonical and microcanonical rate constants via equations (2) and (4) - it is not helpful in a practical sense because a complete state-to-state reactive scattering calculation is required to obtain the 5-matrix. We seek a more direct (and thus presumably more efficient) route to N(E), but without approximation, to which approximations can be incorporated later as needed in specific applications. 

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