The total reaction probability for J=0, J=1, J=2, J=5, and J=10 is
plotted in Fig. 1, where the J=0, J=1, J=2, and J=5 results
were taken from paper I.
In Fig. 3 we plot, as mentioned, the reaction probability as a
together with the total reaction probability for
In paper I we investigated the possibility of decreasing the size of the calculation by leaving out states with a negligible contribution to the reaction probability. We consider an state to be negligible if its contribution to the reaction probability at a certain energy is 3-4orders of magnitude lower than the highest contribution and if this is the case for all energies between 0.8 and 1.8 eV. We concluded that for J=5and lower, no states could be left out. We expected at that time that for higher J it might be possible to leave out states.
In Table I we give the relative contribution to the total reaction probability as a function of the final state, , for J=10, for a number of selected energies. The last row in the table gives the ratio of the largest element of a column with the smallest element of the column (which in this case is the state at all energies). For comparison, we give the corresponding results for J=5, in Table II. As is clear from comparing Tables I and II, the state indeed becomes less important in going from J=5 to J=10, because the ratio of the highest population with the lowest population () increases for each energy point given in Tables I and II. However, it is also clear that that ratio for J=10 is nowhere near the 3-4 orders of magnitude for any energy. Looking at the distribution of the reaction probability over the final states, we also conclude that Coriolis coupling is more important for J=10 than for J=5 in the R-embedding, because for J=5the largest three contributions to the reaction probability accounted for more than 60 %, whereas for J=10 the reaction probability is much more smeared out. In Tables III and IV we tabulated the relative contributions of the final states to the total reaction probability for the J=10, and the J=10, calculations, respectively. Comparing Table I to Table III, we see that qualitatively not much changes. In both cases the lower states are the most important and the highest ratio between the smallest and the largest element is approximately the same (2 orders of magnitude). However, if we look at Table IV, we see that for the J=10, calculation the situation is reversed. Here, the higher states are more important than the lower states, especially at higher energies. It seems unlikely that any state can be left out, since the contribution from all of them is similar. Thus, we conclude (tentatively) that an approximate calculation in which a number of states is left out to make the calculation smaller, will not lead to accurate results. However, we will have to perform the approximate calculations to be absolutely sure about this. Preliminary J=10, calculations show that leaving out the has indeed a sizable effect and cannot be done without significant loss of accuracy. We cannot examine the relative importance of Coriolis coupling as a function of J for calculations done in the r-embedding as straightforwardly, since in that embedding the calculations start in a coherent superposition of all K states.
The series of reaction probabilities from Fig. 1 also allows us to predict the maximum value of J that will have a non-negligible reaction probability. We did the following analysis of our data for each ``bin'' of 0.2 eV between 0.8 eV and 1.8 eV for J>0. For each bin and each J we calculated the average reaction probability. Then, for each bin, we tried a number of different fitting schemes to fit the data as a function of J. Using the fits, we extrapolated to Pr(E)=0. This is of course a very crude way to get an estimate for the maximum J still contributing, but we think that it gives a good idea of the size of that J value.
The best fit for all curves was obtained using a quadratic fitting functional (aJ2+bJ+c form). A slightly worse fit was obtained using an exponential quadratic fitting functional ( form). Unfortunately, not all fitted curves for the quadratic fit had roots on the real axis. However, for the ones that did, PJr(E) became zero between J=16 and J=26. This is remarkably similar to the J values of 15-30 we estimated in paper I based on the maximum impact parameter found in classical trajectory calculations on the H + O2 system.[12,23,24]