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Initial conditions

We start our calculations with a Gaussian distribution in R of the form


 \begin{displaymath}
G(R) = \frac{1}{\sqrt[4]{2\pi\beta}} \exp(-ik_0R) \exp\left[ \frac{-(R-R_0)^2} {4\beta} \right]
\end{displaymath} (16)

where R0 is the center of the wave packet. For the vibrational degree of freedom r, we take the lowest eigenstate of the vibrational Hamiltonian in the potential at R0 for a T-shaped H + O2 geometry. Rotationally, we start in the lowest state, ji =1. This means that for each (ji,J) combination we have $2*\min(j_i,J) +
1$ different $\Omega $-substates. Odd spectroscopic parity has $\min(j_i,J)$ states and even spectroscopic parity has $\min(j_i,J) + 1
$ substates, where spectroscopic parity[65,66] is (-1)J+p. Thus, for the odd spectroscopic parity and ji=1 we start the calculation in the $\Omega=1$ substate. The results for even spectroscopic parity are obtained by performing two calculations, one starting in the $\Omega = 0$ substate and one starting in the $\Omega=1$ state and by subsequent averaging over the results of the two separate calculations (see Ref. [82], p. 204 ff.). Finally, if we want the total reaction probability we have to average over all possible initial (i.e., 3) states. The parameters for the wave packet are given in Table I.


next up previous
Next: Propagation and final analysis Up: Computational aspects Previous: Computational aspects
Anthony J. H. M. Meijer
1998-02-20