CC calculations for

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.

A number of things are immediately clear from the figure. First, the increase in the reaction probability around

From this figure we see that the curves indeed show more resonance structure than the

In Fig. 3 we plot, as mentioned, the reaction probability as a
function of
together with the total reaction probability for
*J*=10.

We see a number of trends continue from our earlier

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.[95] 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 *P*_{r}(*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
(*aJ*^{2}+*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, *P*^{J}_{r}(*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 + O_{2} system.[12,23,24]