Reactive scattering state-selected and cumulative properties

1 Reactive scattering state-selected and cumulative properties 

However, being interested in less detailed information, one might ask for the probability of reaction if the reactants are prepared in a given initial state Up. These initial state-selected reaction probabilities are obtained by summing all state-to-state transition probabilities corresponding to the initial state 

In contrast to S-matrix elements, these observables do not depend on the entire potential energy surface. Pn is infiuenced only by the potential energy surface on the reactant side of the reaction barrier and the region in the vicinity of the barrier. The potential energy surface further on the product side has no impact on pn It only decides upon the specific quantum states in which the products are formed. Thus, the calculation of initial state-selected reaction probabilities only requires the treatment of a reduced portion of the potential energy surface. It causes less numerical effort than a full S-matrix calculation. 

The cumulative reaction probability N E) is an even more averaged quantity. It is the sum of all reaction probabilities of all open channels and does not depend on any specific quantum state of products or reactants  

Since N E) does not refer to any asymptotic state, it is determined only by the dynamics in the vicinity of the reaction barrier. Only the probability to pass the reaction barrier matters in the N E) calculation. Any information about asymptotic states is irrelevant in this context. Thus, restricing the theoretical treatment to the calculation of N E) can drastically reduce the numerical effort. 

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