In this section we present our results for *J*=1, 2, and 5. We will do
that in order of increasing detail, i.e., we start with the reaction
probabilities summed over the possible initial states and we end with
the reaction probability per
substate for a given initial
state .

In Fig. 1 we plot the reaction probability for
*J*=0 and showed that the envelope is basically converged at *T*=30 000
a.u. In Fig. 2 we show a similar plot for
*P*^{J=1}(*E*)
as a function of the propagation time *T*. [Note, that in order to use
this reaction probability in the calculation of a cross section, one
has to multiply it by (2*J*+1)]. This figure also shows that the envelope
of the reaction probability is basically converged at *T*=30 000 a.u.
Therefore, we stopped the calculations for *J*=2 and *J*=5 at
*T*=30 000 a.u, since we are mainly interested in the envelope of the
reaction probability and not in the exact position and widths of the
resonances. For these calculations also more than 97 % of the wave
function has already left the grid at *T*=30 000 a.u. and *P*_{r} (*E*) +
*P*_{nr} (*E*) for the region between 0.85 eV and 1.8 eV never deviates
more than 10^{-3} from 1. Between 0.8 eV and 0.85 eV the deviation is
less than 10^{-2}.

In Fig. 3 we show the total reaction probability
*P*^{J}(*E*) for *J*=0, 1, 2, and 5, averaged over all (3) possible initial
states with the molecule initially in the vibrational state
and
in the rotational state *j*=1. A number of things are immediately clear
from this figure. The division into two parts of the reaction
probability persists at *J*>0. For energies lower than 1.25 eV the
reaction probability is on average independent of energy.
Interestingly, a number of the resonances for *J*=0 persist in the
*J*>0 calculations. This indicates that it might be possible to measure
them in an experimental setup. At energies larger than 1.25 eV the
reaction probability increases rapidly. However, the increase is less
pronounced for *J*>0 than it is for *J*=0. Moreover, at *J*=5 the
reaction probability increases in a linear fashion instead of with a
jump as is the case for *J*=0, 1, and 2. We are currently performing
calculations for *J*=10, 15, and 30 to see if this trend continues for
higher *J* and to see if the reaction probability will go to zero with
higher total angular momentum[84]. This last aspect is
prompted by the fact that classical trajectory calculations suggest
that the reaction has a very small maximum impact parameter between 1
and 2 a.u. (depending on
energy)[25,26,27], which means that
the maximum total angular momentum for *j*_{i}=1 lies somewhere between
15 and 30 (again depending on energy).

In the 3 panels of Fig. 4 we show the reaction
probability for different initial states for *J*=1, 2, and 5,
respectively. The notation
means, that we started the
calculation with the wave packet in the
substate and that
the spectroscopic parity [
(-1)^{J+p} with *p* the parity of the wave
function] was even. Starting in the
substate with odd
spectroscopic parity is designated by
.

In Fig. 4a we plot the reaction probability
for *J*=1,
*P*^{J=1}(*E*). As is clear from this figure, the initial
substate has a distinct influence on the reaction probability.
The
calculation shows a much higher reaction probability
than the
and
calculations. This results
in a lower total reaction probability than for *J*=0. The difference
can be explained to a certain extent using the following classical
model. Initially, there are marked differences in reaction geometry for
the
and the
calculations on
the one hand and
and
calculations on the other hand. In the former case initially the
configuration is ``planar'' (which for *J*=0 of course remains that
way). This means that the molecule is rotating in the plane spanned by
the three atoms. One can imagine that in this configuration it becomes
easier for the H-atom to ``hit'' one of the two O-atoms, leading to a
direct reaction. For
and
the
system is initially in a ``perpendicular'' configuration. This means
that the molecule rotates perpendicular to the instantaneous plane of
the three atoms. If it retains this geometry, it is very hard for the
H-atom to hit one of the O-atoms directly and create products. In fact,
it is more likely that a reaction geometry like this will create an
intermediate complex. Further state-resolved reaction probabilities and
energy-dependent wave functions are needed to resolve this issue.
However, the mechanism given above is consistent with the findings of
Bronikowski *et al.* who concluded on the basis of the populations
of the two
doublet states of the product OH that the planar
configuration was more reactive than the perpendicular configuration at
*E*=1.6 eV[16].

Looking at Fig. 4b and
Fig. 4c, we see that the trends for *J*=1
continue at *J*=2 and *J*=5. The
initial state shows a
higher reaction probability than the other two initial states.
Comparing
to
,
,
and
in
Fig. 5, we see that the reaction probability
goes steadily down. The same holds when comparing the other initial
states for different *J*. This might be due to the fact that the
centrifugal barrier[85] (i.e., the *J*(*J*+1) term in the
Hamiltonian) becomes larger for higher *J*. This suggests that one
might get a good guess for the reaction probability for a specific
initial state for higher total angular momentum by using an approximate
method (see e.g.,
Refs. [86,87,88]), starting from
the *J*=1 calculations. We plan to investigate this issue
further[84].

Looking at Figs. 4 and
5 it is clear that for higher total angular
momentum the resonances get broader and less pronounced. This is the
case not only for the reaction probability, averaged over the initial
states, but also for the reaction probabilities for the separate
initial states. This effect might be caused by the fact that for higher
*J* there are more states available for the wave function to dissipate
into. This also suggests that another frame for doing the calculations
in, e.g., the frame in which the O_{2} bond is the
*z*-axis[89] may not be a better frame in the sense of
conservation of the projection of *J* onto that *z*-axis (this is in
agreement with earlier observations by Pack *et
al.*[34]). We are currently looking into this
issue[84]. On the other hand, given the strong
dependence of the reaction probability on the initial state, it is
clear that
does not scramble as quickly as one might expect.
Knowing that the Coriolis interaction goes to zero as *R*^{-2} when *R*
becomes large, the strong dependence suggests that the Coriolis
interaction becomes non-negligible only in the interaction region. At
higher *J* it might even be possible to leave out a few
substates, if the scrambling is slow enough. In order to investigate
this we put the reaction probability per
substate for
in Table II. For
there is a no
clear trend for the reaction probability as a function of .
For
there seems to be a weak trend for decrease of the
reaction probability with increasing .
For
,
the trend seems to be the reverse. Clearly, *J*=5
is too low to leave out any
states. It will be interesting to
see what happens at higher *J*[84].