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##

Initial Conditions

In all calculations we take and , where is the
initial rotational angular momentum quantum number of O and
its initial vibrational angular momentum. An incoming Gaussian wave packet
is used to describe the initial state in the entrance channel. Because
the quantum number is not determinable experimentally, we do
a calculation for each initially possible and average over
all these calculations.[82] For more details regarding
parameters for the calculations, basis set sizes, etc. we refer to Ref.
th:anth1998. Note that for , the maximum was
increased to 99.

In order to initiate the Chebychev expansion we use the method described in
Ref. th:gray1999. To begin the iteration in Eq. (5)
above, and are required. We take to
simply be the real part of the complex initial wave packet. Since the initial
condition is complex, must be evaluated according to
where is the imaginary part of the initial condition. [61]
The square root operator is also expanded in terms of Chebychev polynomials.
Usually, 200 polynomials are sufficient to converge this expansion.

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Anthony J. H. M. Meijer
2000-10-05