Cancellation puzzle

We are now in a position to discuss the cancellation puzzle in H + H2. We start by considering the state-to-state reaction probabilities computed... 

One would expect that effects of similar magnitude to those shown in Fig. 8 should also appear in the corresponding state-to-state differential and integral cross-sections. However, this is not the case. As already mentioned, there is a considerable amount of cancellation of GP effects in these quantities, which we refer to as the cancellation puzzle. The unexpected cancellations appear in the state-to-state DCS at low impact parameters (i.e., low values of J), and in the state-to-state ICS (including all impact parameters). We now discuss each of these cancellations in turn. 

This observation is the first part of the cancellation puzzle [20, 21, 27, 29]. We know from Section lll.B that we should be able to solve it directly by applying Eq. (19), which will separate out the contributions to the DCS made by the 1-TS and 2-TS reaction paths. That this is true is shown by Fig. 9(b). It is apparent that the main backward concentration of the scattering comes entirely from the 1-TS paths. This is not a surprise, since, by definition, the direct abstraction mechanism mentioned only involves one TS. What is perhaps surprising is that the small lumps in the forward direction, which might have been mistaken for numerical noise, are in fact the products of the 2-TS paths. Since the 1-TS and 2-TS paths scatter their products into completely different regions of space, there is no interference between the amplitudes f (0) and hence no GP effects. 

The second part of the cancellation puzzle concerns the full state-to-state DCS and ICS (i.e., including all the impact parameters). In this case, the GP effects do not cancel in the DCS [26, 27, 29], as is shown in Fig. 10. Instead, they shift the phase of the fine oscillations that are superimposed on the main DCS envelope. Following the above, this indicates that the 1-TS and 2-TS paths scatter into overlapping regions of space, so that the GP produces an effect by changing the sign of the interference between(0) and (0). This is confirmed by Fig. 10b, which shows that the 1-TS and 2-TS DCS do indeed overlap. 

This last point is the second part of the cancellation puzzle, and is soon explained by plotting the phases >l>jjf (9, ) and scattering... 

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