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A. A. Buchachenko
Numerical method for quantum capture probabilities with
applications to ultracold molecular collisions
Abstract
The
simple numerical method proposed by Truhlar and Kuppermann [J. Am. Chem. Soc.
1971. 93, P. 1840] for tunneling problem is adapted for quantum capture
probability calculations in the barrierless molecular processes by imposing
absorbing boundary conditions in the short-range region. It is found that phase
uncertainty inherent to the singular potential problem arising from the
continuation of the long-range potentials to short distances manifests itself
in the oscillatory dependence of the transmission coefficient on the distance
where the boundary condition is applied. Such a behavior permits one the simple
stabilization of the results by taking the mean transmission coefficient. The
method is tested for KRb + KRb reactions and K2 + K vibrational
relaxation at ultralow temperatures using the model dispersion and ab initio-based
adiabatic channel potentials. Good agreement is found with the analytical
models developed for solving the singular problem close to the Bethe-Wigner
threshold and, within the accuracy of capture approximation, with the rigorous
quantum scattering calculations.
Key
words: Barrierless
reactions, capture approximation, statistical adiabatic channel model,
ultracold chemistry
Copyright (C) Chemistry Dept., Moscow State University, 2002
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